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SIMPLE 


ELEMENTS  OF  NAVIGATION. 


BY 


LUCIEN  YOUNG, 

U.  S.  Navy. 


NEW  YORK: 

JOHN    WILEY    &    SONS, 
53  EAST  TENTH  STREET. 

1890. 


Copyright,  1890, 

BY 
JOHN  WILEY  &  SONS. 


DRUMMONB  &  NETT,  FERRIS  BROS., 

Electrot t/pers,  Printers, 

1  to  7  Hague  Street,  326  Pearl  Street, 
New  York.  iNiew  York. 


PREFACE. 


THIS  little  work  is  not  intended  to  supply  any  presumed  de- 
ficiency in  other  books  treating  of  the  same  subject,  but  to 
preserve  one  common  method  throughout  and  to  omit  all 
complicated  mathematical  formulae  and  calculations  beyond 
the  reach  of  men  of  limited  education. 

The  most  simple  elements  of  navigation  only  are  treated  of, 
and  the  tables  added  to  make  the  little  work  complete  in 
everything  necessary  to  navigate  a  vessel  to  any  port  of  the 
globe. 

By  a  study  of  no  other  instructions  than  those  contained  in 
this  little  treatise,  the  nautical  apprentice  can  soon  n't  himself 
for  promotion;  the  merchantman  make  himself  competent  to 
conduct  his  vessel  to  his  destination;  and  the  owner  of  a  yacht, 
with  a  little  trouble,  become  able  to  co-operate  with  his  captain. 
Other  works  are  intended  for  the  use  of  accomplished  mathe- 
maticians or  experienced  navigators. 

» •  » 

111 


CONTENTS. 


CHAPTER  I. 

PAGE 

DEFINITIONS,  DESCRIPTION  AND  >USE  OF  INSTRUMENTS,     ....    1 

CHAPTER   II. 
PILOTING  OR  COASTING,         .  .       .  ....  21 

CHAPTER  HI. 
FINDING  THE  POSITION  BY  DEAD-RECKONING, 24 

CHAPTER  IV. 
DEFINITIONS  AND  DESCRIPTION  OF  INSTRUMENTS  USED  IN  OBSERVATIONS,  35 

CHAPTER  V. 

To  FIND  THE  LATITUDE  BY  OBSERVATION,  .......  40 

CHAPTER  VI. 
To  FIND  THE  LONGITUDE  BY  OBSERVATION,       .       .       .       .       .       .45 

CHAPTER  VII. 
To  FIND  THE  POSITION  BY  A  SUMNER,       .  ....  52 

CHAPTER  VIII. 
To  FIND  THE  TOTAL  ERROR  OF  THE  COMPASS  BY  OBSERVATION,  .       .  GO 

CHAPTER  IX. 

CAUSES  THAT  AFFECT  NAVIGATION  AT  SEA,       .        .        ,        „       ,        .65 

CHAPTER  X. 
AIDS  TO  NAVIGATION, 0  .       .  77 

CHAPTER  XI. 

REGULATIONS  FOR.  PREVENTING  COUJSIONS  AT  SEA,       .       .       .       .98 

v 


VI  CONTEXTS. 

TABLE  I. 

PAGE 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  DEAD-RECKONING,      .  114 

TABLE  II. 
CORRECTIONS  FOR  ALTITUDE,        .  .160 

TABLE  III. 
DECLINATION  OF  THE  SUN ,        .       .       .162 

TABLE  IV. 
EQUATION  OF  TIME,        „....,,,,..  172 

TABLE  V. 

SINES,  COSINES,  SECANTS,  ETC.,  .  .178 


SIMPLE  ELEMENTS  OF  NAVIGATION, 


CHAPTER  I. 
DESCRIPTION  AND  USE  OP  INSTRUMENTS. 

Definitions.  NAVIGATION  is  the  science  which  treats  of 
the  determination  of  a  ship's  position  at  sea  and  the  particular 
direction  a  vessel  should  steer  to  reach  any  given  place.  It 
may  be  said  to  consist  of  two  kinds: 

Firstly,  the  science  of  navigation  by  which  the  position  of 
the  ship  is  determined  from  day  to  day  by  referring  it  to  some 
other  geographical  spot,  such  as  a  known  landmark,  a  deter- 
minate bottom,  or  a  previously  defined  place. 

Secondly,  the  science  by  which  the  position  of  the  ship  is 
determined  from  observations  of  the  heavenly  bodies. 

The  voluminous  works  on  this  subject  are  full  of  difficult 
and  complicated  calculations,  which  only  an  expert  mathema- 
tician could  understand  They  are  beyond  reach  of  the  class 
©f  young  men  of  limited  education,  who  enter  an  apprentice- 
ship either  in  the  merchant  marine  or  the  naval  service.  More- 
over, these  works  are  filled  with  many  methods  by  which  the 
same  problem  is  solved,  embarrassing  to  the  beginner  instead 
of  instructing  him. 

In  order  to  simplify  this  as  much  as  possible  it  is  proposed 
to  imagine  a  vessel  in  port  with  everything  stowed  ready  for 
sea,  and  to  confine  the  problems  to  the  most  common  methods 
in  her  voyage  to  some  other  port  across  the  ocean. 

Use  of  Instruments.  The  first  thing  to  do  on  going  on 
board  is  to  become  acquainted  with  the  use  and  application  of 
such  instruments  as  are  necessary  to  determine  the  distance 
which  the  ship  sails,  the  direction  in  which  she  is  steered,  and 


2  SIMPLE   ELEMENTS   OF   NAVIGATION. 

to  deduce,  from  the  data  these  instruments  furnish,  the  situa- 
tion of  the  ship  at  any  time,  and  to  find  the  distance  and  di- 
rection of  any  place  to  which  it  may  be  required  that  the  ship 
should  be  taken. 

Hand-lead  is  used  to  obtain  soundings  in  shallow  water, 
with  a  view  of  safely  guiding  the  ship  over  shoals,  through 
channels  to  an  anchorage,  or  to  sea;  it  is  in  weight  ranging 
from  five  to  fourteen  pounds. 

Deep-sea  Lead  is  used  to  obtain  soundings  in  deeper  water 
and  to  ascertain  the  nature  of  the  bottom;  it  is  in  weight 
ranging  from  twenty-five  to  one  hundred  pounds;  is  hollow  at 
the  bottom,  for  placing  a  lump  of  tallow  called  the  Arming. 
The  nature  of  the  bottom  is  indicated  by  the  portion  of  the 
bottom  brought  up  in  the  arming. 

In  heaving  this  lead  the  headway  of  the  ship  must  be 
checked  to  get  a  cast;  to  obviate  this  many  ingenious  instru- 
ments have  been  invented  by  which  the  soundings  can  be 
taken  from  a  ship  running  at  full  speed,  in  water  of  any  depth 
not  exceeding  one  hundred  and  fifty  fathoms  (a  fathom  is  six 
feet).  Some  of  these  instruments  register  the  depth  of  water 
descended  through  by  wheel-work  set  in  motion  by  a  fly,  and 
others  by  the  condensation  of  air  contained  in  a  glass  tube  by 
the  pressure  of  water  ;  but  the  most  common  one  in  use  is  the 
Thomson  sounding-machine,  which  has  a  glass  tube  connected 
with  a  sinker,  closed  at  the  top  and  coated  inside  with 
chromate  of  silver ;  the  increased  pressure  at  greater  depths 
drives  the  water  up  the  tube,  and  its  action  leaves  a  white 
mark,  the  position  of  which  is  estimated  by  a  scale,  and  it  is 
independent  of  the  amount  of  line  run  out.  A  small  steel 
wire  is  used  instead  of  a  line,  and  is  coiled  on  a  light  reel. 

Log:  and  Glass  are  used  to  measure  the  rate  of  sailing,  and 
a  timepiece  to  note  the  interval.  The  log  consists  of  several 
parts— chip,  bridle,  line,  and  reel. 

Log-chip  is  a  thin  piece  of  wood,  in  the  form  of  a  sector 
of  about  five  inches  radius,  weighted  on  the  circular  edge  with 
lead  sufficient  to  make  it  swim  upright  in  the  water. 

At  each  of  the  three  corners  is  a  hole,  through  which  two 
of  the  legs  of  the  bridle  are  rove  and  knotted  ;  the  third  leg 
has  a  peg  of  wood  in  the  end,  which,  when  the  log  is  hove,  is 
firmly  pressed  into  the  unoccupied  hole  :  it  remains  thus  while 
the  line  is  running  out,  and  pulls  away  when  the  line  is  being 


DESCRIPTION   AND    USE   OF   INSTRUMENTS. 


hauled  in.     The  legs  of  the  bridle  are  about  two  feet  long, 
and  bent  to  the  outer  end  of  the  log-line. 


LOG-CHIP. 


Log-line  is  a  small  line  of  about  150  fathoms  long,  one  end 
attached  to  the  bridle  and  the  other  fastened  to  a  "  reel," 
over  which  the  log-line  is  wound.  At  about  15  fathoms  from 


LOG-REEL. 

the  chip  a  white  rag  is  placed  to  mark  what  is  called  the 
"  stray-line,"  which  permits  the  chip  to  clear  the  wake  of  the 
ship  or  swash  of  the  propeller.  From  this  rag  inboard  the 
line  is  divided  into  equal  portions  by  bits  of  small  line  through 
the  strands  of  the  log-line,  and  designated  by  the  number  of 
knots  in  each;  hence  are  called  knots.  The  length  of  each  of 
these  divisions  of  the  line  bears  the  same  ratio  to  the  nautical 
mile  that  the  glass  does  to  an  hour.  The  division  of  the  line 
between  the  knots  is  divided  into  tenths,  marked  by  a  small 
string. 


SIMPLE    ELEMENTS   OF    NAVIGATION. 


LOG-GLASS. 


Log-glass  is  an  ordinary  sand-glass  constructed  so  as  to 

permit  the  sand  to  run  from  one  end  to" 
the  other  in  a  certain  time :  those  in 
common  use  are  the  long-glass,  which 
requires  28  seconds,  and  the  short-glass, 
14  seconds,  to  run  through.  The  line  is 
graduated  for  the  long-glass,  and  when 
the  short-glass  is  used  the  knots  indicated 
should  be  doubled. 

Heaving  the  Log.  In  using  these  it 
is  called  heaving  the  log.  One  man 
holds  the  reel  in  a  horizontal  position 
and  another  holds  the  glass  with  the  sand 
down,  while  a  third  takes  the  log-chip 
and  presses  the  peg  into  its  place,  then 
unwinds  a  quantity  of  line,  and  holding  it 
faked  in  his  hand,  calls  "  Clear  glass," 
repeated  by  the  man  holding  the  glass. 
The  one  with  the  line  throws  the  chip 
over  the  lee  quarter  to  clear  the  wake,  and  permits  the  line  to 
run  freely  through  his  hand,  feeding  and  checking  if  neces 
sary,  and  when  the  white  rag  passes  his  hand  he  cries  out 
"Turn  ;"  the  glass  is  then  turned.  The  glass-holder  answers 
Turn,  and  holds  the  glass  up  so  as  to  permit  the  sand  to  run 
through.  The  moment  the  sand  is  run  out  the  glass-holder 
calls  out  "  Up,"  when  the  line  is  checked  and  the  knots  and 
tenths  indicated.  The  log  is  hove  every  hour,  and  should  be 
whenever  the  course  is  changed. 

Log  Adjustments.  The  log  requires  to  be  frequently  ad- 
justed, to  do  which  the  peg  should  be  examined  and  found  to 
fii  sufficiently  tight.  The  log-line  shrinks  unequally,  and  re- 
quires to  be  frequently  verified.  A  convenient  method  is  by 
having  nails  placed  in  the  deck  at  proper  distances  to  measure 
from,  the  line  being  wet  at  the  time.  In  damp  weather  the 
sand  in  the  glass  becomes  wet,  and  is  not  only  retarded,  but 
often  hangs  altogether  :  when  this  is  the  case  the  cork  stopper 
in  the  end  is  removed,  the  sand  taken  out  and  replaced  by  dry, 
or  the  quantity  of  sand  can  be  reduced  or  increased  in  this  way 
when  the  glass  is  in  error.  The  glass  error  is  found  by  com- 
parison with  the  second  hand  of  a  watch  or  a  small  second  pen- 
dulum. A  pendulum  for  comparison  can  easily  be  constructed 


DESCRIPTION    AM)    USE    OF    INSTRUMENTS. 

by  having  hung  from  a  nail  a  small  bullet  by  a  thread 
'inches  long  from  the  centre  of  the  bullet  to  the  nail. 

Many  and  most  efficient  patent  logs  have  been  devised,  and 
have  been  found  very  accurate,  and  have  been  frequently  sub- 
stituted for  the  common  log ;  however,  one  acts  as  a  check  on 
the  other,  and  both  should  be  used.  The  most  common  of 
these  is  the  Taffrail  Log,  which  consists  of  a  rotator  or  fly 
towed  astern  clear  of  the  wake  by  a  line,  and  the  register  is 
attached  to  the  taff  rail.  As  the  fly  is  drawn  through  the  water 
in  a  horizontal  position,  the  motion  is  communicated  by  means 
of  the  connecting  cord  to  the  wheel-work  within  the  register, 
and  sets  in  motion  the  indices.  By  this  means  the  rate  of  the 
ship  can  be  read  off  at  any  time  by  simply  going  to  the  rail 
and  noting  the  interval  it  takes  the  dial  to  make  one  mile. 

Ground-log  is  a  log  adapted  for  use  in  shoal  water  to  ascer- 
tain when  in  doubt  the  set  of  the  current ;  it  consists  of  a  small 
lead  and  a  line  divided  in  the  same  manner  as  the  common 
line.  When  hove,  the  lead  remains  on  the  bottom  and  the 
line  gives  the  combined  motion  of  the  ship  through  the  water 
and  that  of  the  current. 

Compass  denotes  the  direction  sailed,  and  indicates  the 
future  course.  The  compass  is  simply  an  instrument  which 
utilizes  the  directive  powers  of  the  magnet. 

Card  and  Needle.  The  essential  part  of  the  mariner's  com- 
pass consists  of  a  circular  card  upon  which  are  marked  the 
various  points,  and  is  carried  by  a  magnetized  needle  placed 
under  the  line  joining  the  north  and  south  points. 

The  needle  is  freeljr  balanced  upon  a  fine  pivot  rising  from 
the  bottom  of  a  brass  or  copper  bowl  by  means  of  a  small 
agate  cup  fixed  in  the  centre  of  the  needle. 

Compass  Bowl,  containing  the  needle  and  card,  is  carried 
on  gimbals,  so  that  it  may  at  any  time  remain  level  in  what- 
ever direction  the  ship  may  roll  or  pitch.  The  bowl  has  a 
glass  cover,  and  is  fitted  to  carry  lights  to  illuminate  the  face 
of  the  card  at  night.  This  case  and  stand  is  called  the  Bin- 
nacle. 

Lubber's  Point,  Inside  the  bowl  is  painted  a  black  ver- 
tical line,  commonly  called  the  lubber's  point.  The  centre  of 
the  compass  card  and  this  lubber's  point  should  be  in  a  line 
with  the  keel  of  the  vessel,  and  the  point  marked  on  the  card 


6 


SIMPLE    ELEMENTS    OF    NAVIGATION. 


the  ship  is  to  be  steered  should  be  kept  coincident  with  this 
point. 

Points  of  the  Compass.  The  compass  card  is  divided 
into  four  quadrants  by  two  diameters  perpendicular  to  the 
other  ;  the  ends  of  these  diameters  are  called  north,  south,  east, 
and  west,  and  are  marked  N.,  S.,  E.,  W.:  they  are  termed  the 
*'  Cardinal  points."  Each  of  these  quadrants  is  divided 
into  eight  equal  spaces  or  points  ;  hence  there  are  thirty-two 
points  to  the  compass.  These  thirty-two  points  are  in  turn 
subdivided  into  half  and  quarter  points. 

The  following  figure  will  show  the  names  of  these  points. 


MARINER'S  COMPASS. 


The  half  and  quarter  points  are  indicated  from  any  of  the  32 
points  towards  one  of  the  cardinal  points,  thus:  N.  \  E.  means 
half  a  point  from  the  north  towards  the  east.  SW.  |  W. 
means  half  a  point  from  the  southwest  towards  the  west. 


DESCRIPTION   AND    USE   OF    INSTRUMENTS.  7 

Boxing  the  Compass.  To  be  able  to  repeat  the  names  of 
these  points  consecutively  is  called  boxing  the  compass. 

The  compass  card  is  also  divided  into  degrees  for  the  con- 
venience of  taking  bearings,  and  the  following  table  will  give 
the  points,  half  and  quarter  points,  with  the  corresponding 
degrees  from  which  they  can  be  easily  converted  one  to  the 
other. 


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According  to  the  purpose  for  which  the  mariner's  compass 
is  especially  adapted  it  is  named  the  steering,  standard,  and 
azimuth  compass. 


8  SIMPLE    ELEMENTS   OF   NAVIGATION. 

Steering  Compass  is  the  one  placed  in  the  binnacle  near 
the  wheel  to  assist  the  man  at  the  wheel  in  keeping  the  ship's 
head  in  the  prescribed  direction. 

Standard  Compass  is  the  one  placed  on  a  particular  spot 
on  deck  or  above  it  where  the  local  influence  of  the  iron  in  the 
ship  is  the  smallest  and  to  which  the  steering  compass  is  always 
referred. 

Azimuth  Compass  is  the  one  mounted  on  a  stand  in  some 
commanding  position  for  the  purpose  of  taking  bearings,  and 
is  provided  with  a  pair  of  sight  vanes  for  observing  objects. 
The  standard  compass  is  usually  an  azimuth  compass. 

Variation.  The  direction  the  horizontal  needle  assumes 
when  uninfluenced  by  external  causes  is  called  the  magnetic 
north,  and  at  different  times  and  places  does  not  coincide  with 
the  true  north.  The  difference  between  these  two  directions 
measured  in  degrees  is  called  variation.  It  is  said  to  be 
easterly  when  the  north  end  of  the  needle  is  drawn  to  the  east- 
ward, and  westerly  when  it  is  drawn  to  the  westward,  cf  the 
true  north.  The  variation  is  found  on  the  chart. 

Deviation  is  the  term  applied  to  indicate  the  effect  pro- 
duced on  the  compass  by  objects  within  the  ship,  such  as  the 
ship  being  built  of  iron,  laden  with  iron  or  having  certain 
attachments  made  of  iron,  and  local  influences  external  to  the 
ship.  Vertical  iron,  such  as  boat-davits,  iron  stanchions,  smoke- 
stack, etc.,  has  the  greatest  effect  when  the  ship's  head  is  north 
or  south  and  least  when  east  or  west;  and  the  horizontal  pieces 
of  iron,  such  as  deck  beams,  engine  shafts,  etc.,  will  affect  the 
compass  most  at  the  four  points  lying  between  the  cardinal 
points  and  least  at  the  north,  south,  east,  and  west  points. 

The  introduction  of  iron  in  shipbuilding  has  rendered  the 
question  of  deviation  most  important,  and  the  amount  will 
depend  upon  the  direction  in  which  the  ship's  head  lies  while 
building;  if  built  with  her  head  north  and  south  she  will  re- 
ceive a  large  amount  of  induced  magnetism  from  the  hammer- 
ing necessary  and  from  the  earth.  This  magnetism  once 
driven  in,  may  be  increased  or  diminished  by  grating  against 
piers,  striking  sunken  rocks,  or  being  struck  by  a  heavy  sea. 

It  has  also  been  found  the  deviation  is  different  when  the 
vessel  heels  over  on  either  side  to  what  it  was  when  she  is  on 
an  even  keel:  in  northern  latitudes  the  compass  needle  is 
drawn  to  windward  as  the  vessel  heels  over,  and  whenever  the 


DESCRIPTION   AND    USK   OF   IXsTlU  M  KN'TS.  9 

vessel  head  is  E.  or  W.  the  heeling  error  vanishes  and  is 
greater  when  it  is  N.  or  S. 

The  deviation  changes  when  the  ship  proceeds  to  a  different 
latitude,  hence  should  be  frequently  ascertained  and  tables 
constructed  by  the  process  of  swinging  ship  not  only  on  an 
even  keel,  but  also  when  the  ship  is  heeled  over  to  starboard 
and  when  heeled  over  to  port. 

To  Find  the  Deviation.  The  standard  compass  is  placed 
in  its  permanent  position,  and  the  ship  is  taken  to  some  place 
in  smooth  water  and  caused  to  swing  around  that  her  head 
may  be  made  to  come  to  every  point  of  the  compass,  and  as  she 
does  the  deviation  is  ascertained  as  follows: 

I.  By  means  of  buoys  the  true  bearings  of  which,  have  been 
previously  ascertained. 

II.  When  in  an  open  harbor  where  some  fixed  object  at  a 
distance  of  eight  or  ten  miles  can  be  clearly  seen.    Write  down 
the  points  of  the  compass,  and  as  the  ship  swings  around  from 
one  point  to  another  write  down  the  compass  bearing  of  the 
object  opposite  the  point  of  the  compass  towards  which  the 
ship's  head  is  directed.     The  mean  of  two  bearings  on  east  and 
west  by  compass,  or  the  mean  of  all  these  bearings,  will  be  the 
magnetic  bearing  of  the  distant   object   from   the  ship,  the 
difference  of  which  from  each  of  the  bearings  wrill  give  the 
deviation  for  that  point  of  the  ship's  head.     It  is  thus  that  the 
majority  of  deviation  tables  are  constructed. 

III.  When  the  ship  is  in  a  closed  harbor  and  no  distant 
object  can  be  seen,  a  standard  compass  is  taken  on  shore  and 
placed  in  such  a  position  as  to  be  free  from  the  influences 
of  magnetic  attraction,  and  where  it  may  be  seen.    As  the  ship 
swings  around  the  bearing  of  the  compass  on  shore  is  observed 
from  the  ship  as  her  head  comes  to  each  point,  and  at  the  same 
instant,  indicated  by  signals,  the  ship's  compass  is  observed 
from  shore.     The  observations  on  shore  are  first  reversed  to 
bring  them  into  the  same  direction  as  those  taken  from  the 
ship,  and  are  compared  wTith  the  latter;  the  difference  is  the 
deviation.     Should  there  be  a  suspicion  of  local  attraction  to 
the  compass  on  shore  a  plane  table  may  be  used  instead  of  the 
shore  compass. 

IV.  When  at  sea  or  out  of  sight  of  land  if  a  distant  sail  be  in 
sight,  advantage  may  be  taken  of  a  calm  or  light  airs  to  swing 


io 


SIMPLE   ELEMENTS   OF   NAVIGATION. 


ship  by  it  as  in  the  second  case  or  by  the  true  bearing  of  the 
sun  explained  in  Chapter  VIII. 

The  deviation  for  the  ship's  head  at  each  of  the  points  of  the 
compass  having  been  obtained  by  any  of  the  processes  which 
have  been  described,  a  table  of  the  results  should  be  con- 
structed, marking  the  deviation  east  when  the  north  end  of  the 
needle  has  been  drawn  to  the  eastward,  and  west  when  it  has 
been  drawn  to  the  westward,  of  the  magnetic  north.  These 
tables  should  be  constructed  and  made  use  of  even  though  the 
compasses  be  or  be  not  corrected  by  magnets  or  masses  of  iron 
as  is  the  practice  in  iron  ships. 

The  following  is  the  form  of  a  deviation  table: 

DEVIATION  TABLE. 


Ship's  head. 

Deviation. 

Ship's  head. 

Deviation. 

North. 

2  20  E. 

South. 

2  40  W. 

N.  by  E. 

3  40  E. 

S.  by  W. 

3  50  W. 

NNE. 

5  40  E. 

SSW. 

5  SOW. 

NE.  by  N. 

6  50  E. 

SW.  by  S. 

6  00  W. 

NE. 

8  00  E. 

SW. 

6  30  W. 

NE.  by  E. 

8  10  E. 

SW.  by  W. 

7  30  W. 

ENE. 

7  20  E. 

WSW. 

7  SOW. 

E.  by  N. 

7  30  E. 

W.  by  S. 

8   10W. 

East. 

6  40  E. 

West. 

8  00  W. 

E.  by  S. 

5  50  E. 

W.  by  N. 

7  40  W. 

ESE. 

4  30  E. 

WNW. 

6  40  W. 

SE.  by  E. 

3  40  E. 

NW.  by  W. 

5  40  W. 

SE. 

2  00  E. 

NW. 

4  30  W. 

SE.  by  S. 

1  00  E. 

NW.  by  N. 

3  10W. 

SSE. 

0  30  W. 

NNW. 

1   SOW. 

S.  by  E. 

1  30  W. 

N.  by  W. 

0  30  E. 

Leeway  is  an  apparent  error  to  which  the  compass  is  sub- 
jected, and  is  due  to  the  pressure  of  the  wind  and  surge  of  the 
sea  driving  the  vessel  to  leeward,  when  close  hauled  to,  of  the 
direction  by  compass  it  is  intended  she  should  sail.  The 
amount  depends  upon  the  lines  and  trim  of  the  ship,  the  draft 
and  sails  ussd,  or  whether  the  ship  be  as  near  the  wind  as  she 
will  lie.  Leeway  is  estimated  in  points  and  quarter  points  by 
observing  the  wake  astern.  If  the  wind  is  on  the  starboard 
hand  the  leeway  is  to  the  left,  and  if  on  the  port  hand  it  is  to 
the  right. 

Course  of  a  ship  and  the  bearing'  of  an  object  are  terms 
used  with  reference  to  the  standard  compass,  to  the  magnetic 
meHdian,  and  to  the  true  meridian.  The  course  of  the  ship  by 


DESCRIPTION   AND    USE   OF   INSTRUMENTS.         11 

the  standard  compass,  which  is  affected  by  both  deviation  and 
variation,  is  called  the  "compass  course;"  the  course  with 
reference  to  the  magnetic  meridian,  or  the  course  which  would 
be  shown  by  the  compass  on  board  affected  by  variation  only 
and  not  by  the  deviation,  is  called  the  "  correct  magnetic  course." 
The  course  with  reference  to  the  true  meridian  is  called  the 
'•  true  course."  In  the  same  way  the  bearing  of  an  object  may 
be  distinguished  as  the  compass  bearing,  correct  magnetic  bear- 
ing, or  the  true  bearing,  as  the  case  may  be. 

In  any  conversion  from  one  compass  course  to  another,  or 
from  one  compass  bearing  to  another,  whether  the  correction 
is  made  by  applying  the  variation  or  the  deviation,  both  cor- 
rections are  applied  to  the  right  if  easterly,  and  to  the  left  if 
westerly.  Similarly,  where  the  conversion  is  from  one  true 
course  to  another  or  from  one  true  bearing  to  another,  both 
are  applied  to  the  right  if  westerly,  and  to  the  left  if  east- 
erly. The  method  will  appear  in  the  following  examples. 

A  vessel  heads  by  compass  NKE.  \  E.  The  variation  shown 
on  the  chart  is  21°  14'  E.;  find  the  true  course. 

The  compass  course  NNE.  \  E.  or  N.  28°  07'  30"  E. 
Variation  E.       .     .- 21  14  00  right 

The  magnetic  course       .     .     .     .  N.  49  21  30   E. 

From  table  deviation  for  NNE.  \  E.        6  15  00   E.  or  to  right. 

True  course K  55  36  30   E. 

Again  with  the  head  of  the  vessel  at   ESE.   the  variation 
was  shown  on  the  chart  to  be  10°  15'  W.;  find  the  true  course. 
From  compass  table  ESE.  is      .     .     S.  67°  30'  00"  E. 
Variation  from  chart  W.       ...         10    15  00    left. 

True  magnetic  course       .     .     .     .     S.  77   45  00    E. 
Deviation  for  ESE.  from  table  E.  4   30  00    right. 

True  course S.  73    15  00   E. 

The  variation  being  given  by  the  chart  may  be  considered 
as  a  constant  quantity,  but  not  so  with  the  deviation,  which 
may  vary  for  every  point  of  the  ship's  head.  The  frequent 
use  of  the  deviation  table  might  result  in  mistakes,  to  avoid 
which,  it  will  be  better  to  construct  another  table  for  the  con- 
venience of  the  compass  course  or  bearing  to  convert  to  the 
magnetic  course  or  bearing  and  vice  versa.  The  compass 


12 


SIMPLE   ELEMENTS  OF  NAVIGATION". 


course  or  ship's  head  is  written  in  the  first  column,  the  de- 
viation in  the  second  as  found  from  thb  observations  already 
described,  and  the  magnetic  course  in  the  third  column,  thus: 


Ship's 

Devia- 

Magnetic 

Ship's 

Devia- 

Magnetic 

head. 

tion. 

Course 

head. 

tion. 

Course. 

0        / 

o       / 

0        / 

0         / 

North. 

2  20  E. 

N.     2  20  E. 

South. 

2  40  W. 

S.     2  40  E. 

N.  by  E. 

3  40  E. 

N.  14  15  E. 

S.  by  W. 

3  50  W. 

S.     7  25  W. 

NNE. 

5  40  E. 

N.  28  10  E. 

ssw. 

5  20  W. 

S.  17  10  W. 

NE.  by  N. 

6  50  E. 

N.  40  35  E. 

SW.  by  S. 

6  00  W. 

S.  27  45  W. 

NE. 

8  00  E. 

N.  53  00  E. 

SW. 

6  30  W. 

S.  38  30  W. 

NE.  by  E. 

8  10  E. 

N.  64  25  E. 

SW.  by  W. 

7  30  W. 

S.  48  45  W. 

ENE. 

7  20  E. 

N.  74  50  E. 

WSW. 

7  50  W. 

S.  59  40  W. 

E.  by  N. 

7  30  E. 

N.  86  15  E. 

W.  by  S. 

8  10  W. 

S.  70  35  W. 

East. 

6  40  E. 

S.  83  20  E. 

West. 

8  00  W. 

S.  82  00  W. 

E.  by  S. 

5  50  E. 

S.  72  55  E. 

W.  by  N. 

7  40  W. 

N.  86  25  W. 

ESE. 

4  30  E. 

S.  63  00  E. 

WNW. 

6  40  W. 

N.  74  10  W. 

SE.  by  E. 

3  40  E. 

S.  52  35  E. 

NW.  byW. 

5  40  W. 

N.  61  55  W. 

SE. 

2  00  E. 

S.  43  00  E. 

NW. 

4  30  W. 

N.  49  SOW. 

SE.  by  S. 

1  00  E. 

S.  32  45  E. 

NW.  by  N. 

3  10  W. 

N.  36  55  W. 

SSE. 

0  30  W. 

S.  23  00  E. 

NNW. 

1  50  W. 

N.  24  20  W. 

S.  by  E. 

1  SOW. 

S.  12  45  E. 

N.  by  W. 

0  30  E. 

N.  10  45  W. 

To  obtain  the  correct  magnetic  course  from  the  compass 
course,  look  in  the  first  column  for  the  compass  course,  the 
second  column  gives  the  deviation  when  the  vessel's  head  is 
on  that  point,  and  the  third  column  will  be  found  the  mag- 
netic course. 

In  order  to  correct  any  bearings  taken  by  the  compass  the 
table  is  to  be  entered  with  the  direction  of  the  ship's  head  at 
that  time  in  the  first  column,  and  corresponding  thereto  in 
the  second  column  will  be  found  the  amount  of  deviation  to 
be  applied,  as  per  example  :  If  a  ship's  head  is  NNE.  the 
bearing  of  two  islands  be  SE.  and  W.  by  S.  by  the  compass. 
In  the  second  column  of  the  table  and  opposite  to  NNE.  the 
deviation  is  5°  40'  E. ;  applying  this  deviation  to  the  right  the 
correct  magnetic  bearing  of  the  two  islands  will  be  S.  39°  20' 
E.,  and  S.  83°  55'  W.,  or  roughly  in  points  SE.  |E.  and 
W.*S. 

The  Chart  is  used  to  plot  the  position  of  the  ship  at  any 
time  and  refer  it  to  other  known  objects.  Its  construction 
has  especial  reference  to  the  requirements  of  navigation. 
Thus  the  chart  may  be  required  for  coasting  purposes,  in 
which  case  the  harbor  or  coast  charts  are  used,  upon  which 
are  marked  with  great  accuracy,  the  rocks,  shoals,  local  cur- 


DESCRIPTION    AND    USE   OF   INSTRUMENTS.         13 

rents,  nature  of  the  tides,  soundings  and  channels  as  well  as 
the  different  aids  to  navigation  and  their  bearings. 

For  off  shore  cruising  the  Mercator  Chart  possesses  so 
many  advantages  that  it  is  universally  adopted  for  sea  pur- 
poses. 

For  the  purposes  of  navigation  and  in  order  that  the  rela- 
tive positions  of  places  on  the  earth's  surface  may  be  laid 
down  and  quickly  found,  certain  lines  are  supposed  to  be 
drawn  upon  the  sphere. 

These  imaginary  lines  of  reference  are  called  Parallels  of 
Latitude  and  Meridians,  and  when  these  are  known  for  any 
given  place  its  position  upon  the  globe  is  precisely  determined 
by  their  intersection. 

The  extremities  of  the  axes  of  the  earth  are  called  the  Poles, 
and  the  great  circles  passing  through  these  poles  are  called 
Meridians.  It  is  customary  with  us  to  call  that  meridian 
which  passes  through  Greenwich  the  First  or  Prime  Merid- 
ian. 

The  great  circle  drawn  around  the  earth  at  equal  distance 
from  the  poles,  and  perpendicular  to  the  meridians,  is  called 
the  Equator. 

The  equator  and  the  prime  meridian  are  the  first  lines  of 
reference  from  which  latitude  and  longitude  are  measured. 

Latitude.  The  lines  of  latitude  run  due  east  and  west, 
and  are  small  circles  of  the  sphere  drawn  parallel  to  the 
equator;  we  may  conceive  one  of  these  drawn  through  every 
place.  The  portion  of  a  meridian  intercepted  between  a 
place  and  the  equator  is  called  the  latitude,  and  is  denomi- 
nated north  or  south  as  the  place  is  north  or  south  of  the 
equator. 

Longitude.  The  longitude  of  a  place  is  the  portion  of  the 
equator  intercepted  between  the  prime  meridian  and  the 
meridian  passing  over  the  place  ;  is  east  or  west  according  as 
the  place  is  situated  east  or  west  of  the  prime  meridian. 

As  every  circle  large  or  small  is  divided  into  360  parts 
called  degrees,  it  will  be  seen  the  equator  and  poles  divide 
every  meridian  into  four  equal  parts ;  therefore  the  greatest 
latitude  a  place  can  have  is  90  degrees,  and  again  the  prime 
meridian  divides  the  parallels  of  latitude  into  two  equal  parts, 
making  180  degrees  the  greatest  longitude  a  place  can  have. 
Each  of  these  degrees  is  divided  into  60  minutes  and  the 


14  SIMPLE    ELEMENTS   OF   NAVIGATION". 

minutes  into  60  seconds.  The  minutes  of  the  equator  and  of 
the  meridians  are  each  nearly  6080  feet  long,  and  are  called 
Nautical  or  Sea-miles. 

The  parallels  of  latitude  being  small  circles  and  decreasing 
in  size  the  nearer  they  approach  the  poles,  while  the  meridians 
come  together  at  the  poles,  it  would  be  difficult  to  construct 
a  chart  easy  to  use  in  practice.  However,  upon  the  principles 
of  Mercator  a  chart  is  constructed  upon  which  the  meridians 
are  represented  as  being  parallel  to  each  other  during  their 
whole  length,  and  the  distance  between  the  parallels  of  lati- 
tude is  increased  in  the  same  proportion  the  nearer  they  ap- 
proach the  poles.  This  enables  a  course  from  one  place  to 
another  to  be  laid  down  by  a  straight  line  between  them,  and 
the  distance  is  obtained  from  the  scale  to  the  side  of  the  chart 
as  nearly  opposite  the  two  places  as  possible. 

All  charts  are  engraved  true  north  and  south,  east  and  west, 
and  in  all  the  charts  furnished  by  the  Hydrographic  Office  the 
true  compass  is  engraved  in  various  places  and  the  bearings 
given  are  the  true  bearings.  Lines  of  variation  are  drawn 
upon  the  chart  or  the  variation  is  given  marked  with  each 
compass  on  the  chart. 

Currents  are  marked  on  the  chart  by  an  arrow  with  two 
feathers  pointing  in  the  direction  towards  which  it  sets  1K>  > 
And  the  drift  or  rate  per  hour  at  which  it  moves  is  marked 
in  knots  close  to  the  arrow. 

The  set  of  the  tide  is  marked  on  the  chart  by  an  arrow 
feathered  on  one  side  only  for  the  flood  '^mmtf  >  and  by  an 
arrow  without  feathers  for  the  ebb  tide > 

The  tide  is  spoken  of  as  flood  when  the  water  is  rising,  and 
as  ebb  when  the  water  is  falling;  and  to  show  when  either 
occur,  the  time  of  high  water  at  the  full  and  change,  that  is 
to  say  at  full  moon  and  new  moon,  is  given  at  the  most  impor- 
tant places  on  the  chart.  The  hours  are  marked  in  Roman  and 
the  minutes  in  ordinary  figures,  thus,  VII  h.  50  m.  For  any 
particular  spot  this  time  of  high  water  at  the  full  and  change 
may  be  considered  practically  constant.  Any  almanac  will 
give  the  moon's  age;  but  by  a  little  practice  it  may  be  guessed 
within  a  day.  When  it  looks  like  a  D  it  is  increasing  or  wax- 
ing, and  when  it  looks  like  a  C  it  is  decreasing  or  waning. 

The  rise  of  Spring:  Tides  or  those  which  occur  near  the 
full  and  change  of  the  moon,  and  the  rise  of  the  Neap  Tides 
or  those  which  occur  near  the  1st  and  3d  quarters  of  the 


TIME   OF   HIGH    WATER.  15 

moon,  are  given  in  feet.  Sometimes  this  information  about 
the  tides  is  given  in  a  table  on  the  chart. 

Tides  are  caused  chiefly  by  the  moon,  and  as  the  moon  is 
about  50  minutes  later  every  24  hours  in  comiug  over  the 
same  spot  of  the  earth,  the  time  of  high  water  will  be  about 
50  minutes  later  every  day.  In  most  places  the  tide  rises 
twice  in  every  24  hours,  which  would  make  a  regular  interval 
of  12  hours  between  the  times  of  successive  high  water,  and 
25  minutes  additional  for  the  retardation  of  the  moon. 

The  calculations  for  finding  the  exact  time  of  high  water 
are  puzzling,  and  require  tables  that  may  not  be  at  hand. 
It  is  important  to  know  the  time,  because  in  many  channels 
it  is  only  at  high  water  that  a  vessel  can  get  over  the  bar. 
First  find  the  number  of  days  from  the  last  new  or  full  moon, 
multiply  this  by  50,  the  number  of  minutes  that  the  high  tide 
is  delayed  each  day,  and  add  the  product  in  hours  and  min- 
utes to  the  time  of  high  water  given  on  the  chart,  A.M  or 
P.M.,  as  the  case  may  be.  Or  you  can  reckon  forward  the 
number  of  days  to  the  next  new  or  full  moon,  and  then  sub- 
tract the  product  from  the  time  on  the  chart.  The  question 
whether  you  will  reckon  backwards  or  forwards  depends  on 
whether  the  last  new  or  full  moon,  or  the  coming  new  or  full 
moon,  is  furthest  off.  Of  course  you  wTill  reckon  to  which- 
ever is  nearest. 

The  time  of  high  water  obtained  in  this  way  may  be  de- 
pended upon  within  the  hour,  yet  it  may  be  out  at  times  as 
much  as  two  hours.  The  greatest;  error  will  occur  during 
neap  tides,  hence  by  subtracting  one  hour  from  the  time  of 
high  wraterat  neap  tide,  will  diminish  this  error.  The  follow- 
ing table  will  show  how  the  rule  works  : 


Before  the  new  or  full  moon. 

Subtract. 

For  1  day    

hrs.  min. 
0        50 
1        40 
2        30 
3        20 
4        10 
5        00 
5        50* 

2    "       

3    "       

4    "       

5    "       .               

6    "       

7    "       

After  the  new  or  full  moon  add  the  above 

times. 

*  At  neap  tide  subtract  1  h.  from  time  of  high  water. 


16  SIMPLE    ELEMENTS    OF   NAVIGATION. 

For  example.  The  high  water  at  full  and  change  at  Old 
Point  Comfort  is  8.46;  at  what  time  will  it  be  high  water  on 
the  10th  June,  1888  ? 

From  any  almanac  we  find  that  in  June  the  new  moon 
occurs  on  the  9th  in  the  afternoon,  and  the  full  moon  on  the 
23d  in  the  afternoon.  Now  the  10th  of  June  is  one  day  after 
the  new  moon,  therefore  to  the  above  table  we  must  add  50 
minutes  to  8.46,  which  gives  9.36  P.M.  as  the  time  of  high 
water  on  the  10th  of  June. 

Again,  what  time  will  it  be  high  water  on  the  20th  of  June  ? 
Now  the  20th  of  June  is  three  days  before  the  full  moon, 
therefore,  from  the  abore  table  we  must  subtract  2.30  from 
8.46,  which  gives  6.16  P.M.  as  the  time  of  high  water  on  the 
20th  of  June. 

The  soundings  marked  on  the  chart  are  reduced  to  mean 
low  water,  and  are  generally  given  on  the  plain  section  in 
fathoms  (of  six  feet)  and  fractions  of  a  fathom;  and  on  the 
shaded  surface  in  feet  and  fractions  of  a  foot. 

Large  charts  are  constructed  for  each  ocean  upon  a  too 
small  scale  for  practical  purposes  when  near  shore,  but  to 
facilitate  their  use  they  are  divided  into  marked  sections  ac- 
companied with  an  index  chart.  These  sectional  charts  have 
engraved  upon  them  at  the  most  convenient  places,  divided 
from  the  rest  of  the  chart,  a  plan  of  the  most  important  har- 
bors upon  a  scale  large  enough  for  the  various  marks  to  be  in- 
dicated and  the  nature  of  the  channel  understood. 

With  the  chart  use  is  made  of  a  pair  of  dividers  and  paral- 
lel rulers,  the  application  of  which  will  be  shown  in  working 
some  of  the  problems. 


17 


SIGNS  AND  ABBREVIATIONS  MARKED  ON  THE  CHART. 


Nature  of  the  Bottom. 


General  Abbreviation. 


b    blue 

blk black 

br brown 

brk broken 

c  coarse 

cl clay 

crl — coral 

d dark 

f fine 

g gravel 

gn green 

grd . .  .ground 

gj  gray 

h hard 

m mud 

oys oysters 

oz ooze 

peb pebbles 

r rock 

rot     rotten 

s sand 

sft soft 

sb shells 

spk speckled 

st  stones 

stf stiff 

w.  white 

wd weed 

y yellow 


An ...   anchorage 

Bk bank 

C cape 

Ch church 

Chan channel 

Cr -creek 

Fms „ fathoms 

Ft feet  or  foot 

H.  W high  water 

H.  W.  F.  &  C high  water,  full  and  change 

I island 

Lat latitude 

Long longitude 

Lt light 

Lt.  F  light  fixed 

Lt.  Fl light  flashing 

Lt.  Int light  intermittent 

Lt.  Rev light  revolving 

Lt .  Fig light  floating 

Lt.  Occ light  occulting 

Lt.  Alt light  alternating 

L.  W low  water 

Mt mountain 

Np neaps 

Obs .  Spot observation  spot 

Pk peak 

Pt point 

R river 

Rf reef 

R rock 

Sh shoal 

Sp spring 

Str strait 

Var variation 

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18 


SIMPLE   ELEMENTS   OF   NAVIGATION. 


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20  SIMPLE   ELEMENTS   OF   NAVIGATION. 


EXAMPLES. 

I.  The  compass  course  is  ESE.,  or  S.  67°  30'  00"  E.     The 
variation  and  deviation  2f  points  E.,  leeway  f   points  right. 
What  is  the  true  course?  Am.  S.  28°  07'  00"  E. 

II.  The  compass  course  is  SSW.,  the  variation  being  1  point 
easterly.     Find  the  true  course.  Am.  SW.  by  S. 

III.  An  object  bore  by  compass  NE.  by  E.  |  E.,  the  varia- 
tion being  1£  westerly.    Find  its  true  bearing.    Ans.  NE.  %  N. 

IV.  Compass  course  is  S.  and   the  wind  is  NW.,  giving  f 
points  leeway,  variation  1  point  E.  and  the  deviation  £  point 
W.     Find  the  true  course.  Ans.  S. 

V.  The  true  course  is  S.  by  W. ;  variation  is  2  points  W. ; 
deviation  is  5°  W.      Find  compass  course. 

Ans.  S.  62°  30'  00"  E. 

VI.  The  true  course  is  W.  by  S.,  and  the  variation  is  11°  15' 
E.,  deviation  is  9°  W.,  wind  NNE.,  leeway  of  2  points.     Find 
the  true  course.  Ans.  N.  81°  W. 

VII.  The  compass  course  is  SSE.,  with  variation  2  points 
W.,  and  deviation  5°  E.,  the  wind  on  the  left  hand  giving  3 
points  leeway.     Find  the  true  course.          Ans.  S.  6°  15'  E. 

VIII.  The  compass  course  is  NE. ,  and  variation  is  2  points 
E.,  deviation  2°  E.,  wind  on  the  right  hand  giving  3  points 
leeway.     Find  the  true  course.  Ans.  N.  38°  45'  E. 


PILOTING    OR   COASTLXG.  21 


CHAPTER  II. 
PILOTING  OR  COASTING. 

HAVING  become  thoroughly  familiar  with  the  instruments 
described ,  the  ship  is  gotten  underway  and  taken  down  the 
harbor  or  bay  for  an  offing  at  sea.  In  doing  this  the  rudest 
manner  of  navigation  is  used,  called  Piloting"  or  Coasting1, 
which  requires  only  a  local  knowledge  of  the  shore  and  its 
adjacent  waters,  together  with  the  location  of  marks  placed  to 
aid  navigation,  all  of  which  are  given  in  the  charts. 

The  effect  of  the  tides  and  local  currents  along  the  shore 
is  most  treacherous,  and  may  at  any  time  cause  the  ship  to 
be  drifted  out  of  the  channel  or  into  a  dangerous  position 
to  some  reef  or  shoal,  to  avoid  which  the  actual  position  is 
often  a  matter  of  vital  importance.  A  frequent  cast  of  lead 
may  give  warning,  and  should  be  constantly  kept  going  when- 
ever on  soundings,  and  carefully  taken.  If  the  ship  is  be- 
calmed the  ground  log  will  indicate  the  direction  and  rate  of 
drift. 

Cross-bearings.  When  two  known  objects  are  in  sight 
the  ship's  position  is  found  by  cross-bearings.  Thus,  as  the 
ship  proceeds  down  the  channel  the  starting-point  buoy  bore 
per  compass  ENE.,  and  a  lighthouse  N.  f  W.,  while  the  ship's 
head  was  NW.  Enter  the  deviation  table,  which  should 
always  be  at  hand  in  a  little  note-book,  with  the  ship's  head 
KW.  in  the  first  column,  and  the  deviation  to  be  applied  in 
the  second  column  is  4°  30'  W.  Applying  this  to  the  left 
will  give  the  magnetic  bearings  ;  and  if  the  variation  was  5° 
E.,  apply  it  to  the  right,  and  the  true  bearings  will  be: 

Starting  Buoy  Lighthouse. 

By  compass N.  67°  30'  E.        K  8°  20'  W. 

Deviation  W.  4°  30' left  4°  30' left 


Magnetic  bearing. .  .N.  63°  00'  E.        N.  12°  50'  W. 
Variation  E 5°  00'  right          5°  00'  right 


True  bearing K  683  00'  E.         N.  7°  50'  W. 


SIMPLE   ELEMENTS   Otf   NAVIGATION. 

Apply  the  parallel  ruler  to  the  engraved  compass  on  the 
chart  lying  along  N.  68°  E.  and  the  centre  of  the  compass; 
then  work  the  ruler  until  the  edge  touches  the  start  buoy  and 
draw  a  pencil  line  along  its  edge  on  the  chart.  Apply  in  like 
manner  the  N.  7°  50'  W.  line  to  the  lighthouse.  Where  these 
two  lines  cut  each  other  will  be  the  position  of  the  vessel. 

The  bearings  of  these  two  points  should  not  be  too  near  each 
other,  for  then  the  lines  would  have  a  bad  intersection;  but 
if  the  two  objects  be  in  line,  it  is  of  great  advantage,  especially 
so  when  in  the  direction  the  ship  is  steering,  as  their  separa- 
tion will  indicate  a  deviation  from  the  channel. 

Where  the  two  lines  cross,  or  the  position  of  the  ship,  it  is 
marked  by  a  little  pencil  cross  with  the  hour  and  date  thus, 

X  2iI/3»  to  identify  it,  which  means  the  ship  was  in  this  posi- 
tion at  2  in  the  afternoon  of  March  12. 

Bow  and  Quarter  Bearing.  A  very  simple  means  of  find- 
ing the  constant  position  of  the  ship  is  by  what  is  known 
as  the  bow  and  quarter  bearing.  Take  the  bearing  of  one 
known  object  on  shore  when  it  is  on  the  bow  and  measure  the 
distance  by  log  till  it  bears  abeam;  then  the  distance,  should 
there  be  no  current,  will  be  the  distance  of  the  object  when 
abeam. 

Bearing  of  One  Object.  When  it  is  impossible  to  get  a 
bow  and  quarter  bearing,  such  as  having  to  change  the  course, 
the  ship's  position  can  be  found  by  taking  the  bearing  of  the 
point  when  not  in  the  direction  the  ship  is  sailing,  and  when 
the  bearing  has  changed  at  least  3  points  take  a  second  bear- 
ing. Lay  off  from  the  given  point  the  two  bearings  corrected 
j  for  variation  and  deviation,  and,  after  laying  the  parallel  ruler 
in  the  direction  of  the  true  course,  take  the  distance  sailed  in 
the  dividers  and  move  the  ruler  towards  the  given  point  till 
the  distance  tits  exactly  between  the  two  lines  and  draw  a 
pencil  line.  At  the  two  points  of  intersection  will  be  the  first 
and  second  position  of  the  ship. 

Whenever  the  vessel  is  in  theViciuity  of  land  this  method 
should  frequently  be  used  as  a  check  to  the  influence  of  un- 
known currents. 

By  Sailing  Directions  or  Chart.  When  the  channel  has 
long  stretches  winding  between  shoals  or  among  islands,  the 
sailing  directions  or  chart  gives  the  true  or  magnetic  courses 
and  bearings.  Suppose  they  are  magnetic,  such  as  steer 


PILOTING   Oil   COASTING.  23 

NE.,  till  a  certain  object  bears  N.  by  W.,  and  then  steer  E. 
till  another  object  bears  SW.  In  such  a  case  the  magnetic 
course  and  bearing  are  given  to  rind  the  compass  course  and 
bearing  of  the  object.  Look  in  the  3d  column  of  the  devia- 
tion table  for  the  magnetic  course,  expressed  in  degrees  and 
minutes. 

If  it  be  not  one  of  the  courses  it  will  lie  between  two  of 
them,  and  the  corresponding  compass  course  will  lie  between 
two  courses  in  the  1st  column  and  may  be  found  by  estimat- 
ing. To  find  the  compass  bearing  look  in  the  3d  column  for 
the  magnetic  course;  opposite  to  it  in  the  2d  column  will  be 
the  deviation  on  that  course. 

Apply  this  deviation  to  the  magnetic  bearing  to  the  left  if 
the  deviation  is  easterly  and  to  the  right  if  westerly. 

EXAMPLE. 

Suppose  the  chart  should  give  directions  to  steer  E.  till  a 
certain  objectjaore  N.  by  W.,  then  steer  SE.  till  another  object 
bore  SSW.  magnetic. 

In  column  3,  when  the  course  was  E. ,  the  deviation  was  be- 
tween 6°  40'  E.  and  7°  30'  E.,  or  nearly  i  point  E.  Applying 
this  to  the  left  of  the  first  course,  the  vessel  should  steer  E.  i  N. 
by  the  compass  till  the  first  object  bore  by  compass  N.  by  W. 
£  W.  So  from  column  3  with  the  course  SE.  the  deviation  is 
between  2°  00'  E.  and  3°  40'  E.,  or  nearly  i  point  E.  Apply- 
ing this  to  the  left  of  the  second  course,  the  vessel  should 
steer  SE.  £  E.  till  the  second  object  bore  by  compass  S.  by  W. 
f  W. 

In  going  around  a  point  and  no  channel  marked  out,  select 
several  spots  on  the  chart,  the  connection  of  which  will  per 
mit  the  line  joining  them  to  pass  over  safe  soundings.  With 
the  points  of  the  dividers  on  two  of  the  spots,  transfer  them  to 
the  scale  and  measure  the  distance  ;  then  with  the  edge  of  the 
parallel  ruler  along  the  line,  move  it  to  the  nearest  compass, 
and  the  point  over  which  the  edge  comes  will  be  the  true 
course;  correct  this  for  variation  and  deviation  to  get  the  com. 
pass  course.  Put  the  ship's  head  on  that  course  and  sail  the 
distance,  when  the  same  process  will  be  repeated. 

Should  the  ship  be  shut  in  by  a  fog  or  snow  storm  for  a 
time   out   of   sight  of  laud,  the   channel  and  nature  of  the 


24  SIMPLE    ELEMENTS   OF   NAVIGATION. 

bottom,  as  well  as  soundings  by  the  hand  or  deep-sea  lead, 
will  give  a  close  approximation  to  the  position  of  the  ship. 

When  the  latitude  and  longitude  are  known,  the  position  of 
the  ship  is  plotted  on  the  chart  by  laying  the  parallel  ruler 
even  with  the  nearest  parallel  of  latitude  marked  on  the  side 
of  the  chart,  and  after  moving  it  up  to  the  given  latitude  draw 
a  pencil  line,  which  will  represent  the  latitude  of  the  ship; 
then  measure  with  the  dividers  at  the  top  and  bottom  of  the 
chart  the  distance  from  the  nearest  meridian  to  the  given 
longitude,  which,  set  off  on  the  parallel  previously  drawn  with 
pencil,  will  be  the  ship's  position. 

To  Verify  the  Deviation  Table.  When  the  vessel  was 
swung  in  the  harbor  for  deviation  there  might  have  been 
some  local  attraction  unknown  which  would  of  course  affect 
the  local  deviation  table.  To  ascertain  this,  it  is  an  excellent 
opportunity,  as  the  vessel  proceeds  along  the  various  courses  in 
the  channel,  to  verify  the  deviation  table  by  frequent  bearings 
of  known  objects  on  shore,  or  when  two  objects  come  in  line. 
The  chart  will  give  their  true  bearings,  and  when  converted  to 
the  compass  bearings  by  the  application  of  variation  and  devia- 
tion there  should  be  no  difference  between  this  bearing  and 
the  compass;  if  so,  the  deviation  is  wrong  and  must  be  corrected 
before  going  to  sea. 


CHAPTER  III. 

9 

DEAD-RECKONING. 

Shaping  the  Course.  The  vessel  having  now  arrived  at 
the  point  where  it  becomes  necessary  to  commence  her  voy- 
age at  sea,  the  bearing  and  distance  to  the  point  it  is  intended 
to  take  the  vessel  are  found  from  the  chart  by  laying  the  ruler 
with  the  edge  along  the  two  places,  then  transfer  the  ruler  to  the 
nearest  compass  on  the  chart,  which  will  give  the  true  bearing. 
Correct  the  true  bearing  for  variation  and  deviation  to  the 
left  if  easterly,  and  to  the  right  if  westerly,  for  the  compass 
course,  and  the  ship  is  kept  as  near  that  course  as  the  wind  and 
other  circumstances  will  admit. 


DEAD-RECKON1N<J.  25 

With  the  dividers,  measure  the  distance  on  the  scale  to  the 
side  of  the  chart  as  nearly  opposite  the  two  places  as  it  is  pos- 
sible. 

If  islands,  capes,  and  headlands  intervene,  it  will  be  neces- 
sary to  find  several  courses  and  distances  in  the  same  way. 
This  is  called  Shaping  the  Course. 

Taking-  the  Departure.  When  just  about  to  leave  the 
laud  take  the  bearing  of  some  known  object,  such  as  a  light- 
house or  headland,  by  the  compass  and  estimate  the  distance 
hy  eye,  or  the  bearing  and  distance  of  the  object  from  the  ship. 
This  may  be  found  by  one  of  the  processes  already  described. 
This  is  called  Taking  the  Departure. 

Log-slate.  The  opposite  point  to  that  on  which  the  object 
bears  is  considered  the  first  course,  and  the  distance  of  the  ob- 
ject as  the  first  distance  sailed  from  the  place  and  is  noted  on 
the  log-slate.  This  Log  slate  is  a  memorandum  board  or  book 
properly  ruled  for  the  hours  of  the  day,  distance  made  by  the 
log,  courses  steered  by  the  compass  and  the  direction  of  the 
wind,  leeway,  variation,  and  deviation,  as  well  as  remarks  of 
all  causes  affecting  the  sailing  of  the  ship. 

Log-book.  The  other  courses  and  distances  made  during 
the  day  being  determined  by  the  compass  and  the  log  are  sev- 
erally entered  in  the  log-slate  at  the  end  of  each  hour,  and  after- 
wards copied  into  a  book  similarly  ruled,  called  the  Log-book. 

It  must  be  borne  in  mind  that  the  standard  compass  is  the 
compass  from  which  all  courses  for  the  log-slate  are  taken. 
In  steering,  the  course  is  taken  from  the  standard  compass 
and  the  man  at  the  wheel  given  his  course  for  the  steering 
compass  by  a  careful  comparison.  As  the  vessel  proceeds  on 
her  course  frequent  comparisons  should  be  made  between 
these  two  compasses. 

In  a  violent  gale  and  heavy  sea,  when  it  would  be  dangerous 
to  carry  sail,  it  is  usual  to  put  the  ship  close  to  the  wind  with 
just  sufficient  sail  to  prevent  the  vessel  from  rolling  too  much. 
In  this  condition  the  vessel  will  come  up  and  fall  off,  and  the 
points  to  which  her  head  comes  up  and  falls  off  must  be  noted, 
and  the  middle  point  between  the  two  taken  as  the  course  to 
enter  in  the  log- slate. 

If  there  should  be  a  set  and  drift  of  a  current  it  is  to  be  en- 
tered as  a  course  and  distance,  and  treated  the  same  as  any 
course  and  distance. 


26  SIMPLE   ELEMENTS   OF   NAVIGATION. 

Dead-reckoning.  The  process  by  which  the  position  of 
the  ship  is  found  from  the  data  given  in  the  log-book  is  called 
Dead-reckoning.  By  means  of  this  dead-reckoning  the  latitude 
and  longitude  are  found,  hence  the  position  of  the  ship.  It  is 
usual  to  obtain  the  position  at  8  A.M.,  12  M..  and  8  P.M.  of  each 
day,  and  more  frequently  when  approaching  land  or  danger. 

The  process  by  which  this  is  accomplished  is,  first,  correct 
the  several  courses  in  the  log-book  for  the  variation,  deviation, 
and  leeway  opposite  to  each  course.  Construct  a  table  in  the 
Work-book,  in  which  all  data  in  navigation  should  be  pre- 
served during  the  entire  voyage.  In  the  first  column  of  this 
table  enter  each  true  course,  and  in  the  second  column  the  dis- 
tance run  on  each  course,  found  by  summing  up  the  knots 
and  tenths  sailed  by  the  ship  on  each  course. 

Find  in  Table  I  the  courses  at  the  top  or  bottom  of  the  page 
given  in  degrees,  the  difference  of  latitude  and  the  depar- 
ture corresponding  to  each  course  and  distance,  and  place 
them  in  their  respective  columns;  then  the  difference  between 
the  sums  of  the  northings  and  southings  will  be  the  differ- 
ence of  latitude  made  good  of  the  same  name  as  the  greater. 

Seek  in  the  same  table  until  the  difference  of  latitude  and 
departure  are  found  together  in  their  respective  columns; 
opposite  to  these  in  the  distance  column  will  be  the  distance 
made  good. 

At  the  top  or  bottom  of  the  page,  according  as  the  departure 
is  less  or  greater  than  the  difference  of  latitude,  will  be  found 
the  course  made  good. 

If  the  latitude  of  the  object  from  which  the  departure  was 
taken  or  the  latitude  of  a  former  position  be  of  the  same 
name  as  the  difference  of  latitude  found,  add  them  together ; 
but  if  of  different  names  take  their  difference  ;  the  sum  or  re- 
mainder will  be  the  latitude  in  of  the  same  name  as  the 
greater. 

As  departure  is  the  lineal  distance  between  two  meridians 
measured  upon  a  parallel  of  latitude,  it  is  less  than  the  differ- 
ence of  longitude,  which  is  measured  upon  the  equator;  so  to 
find  the  difference  of  longitude  take  the  middle  latitude  between 
the  two  places  which  take  as  a  course  in  Table  I.,  and  seek  for 
the  departure  in  the  difference  of  latitude  column;  then  will 
the  corresponding  distance  be  the  difference  of  longitude  of  the 
same  name  as  the  departure.  If  the  longitude  of  the  previous 


DEAD-RECKONING. 


position  be  of  the  same  name  as  the  difference  of  longitude  add 
them  together,  bat  if  of  different  names  take  their  difference; 
the  sum  or  difference  will  be  the  longitude  in  of  the  same  name 
as  the  greater. 

The  intersection  of  the  latitude  and  longitude  found  on  the 
chart  will  be  the  position  of  the  ship,  from  which  the  bearing 
and  distance  of  the  port  or  other  object  can  again  be  found. 
It  is  especially  important  to  always  find  the  bearing  and  dis- 
tance of  any  supposed  or  real  danger  whenever  the  position  of 
the  ship  is  plotted 

EXAMPLE. 

When  the  ship  was  about  to  leave  the  land  on  July  15th,  the 
departure  was  taken  from  Cape  Henry  light-house,  which  bore 
per  compass  NNW.,  distance  20  miles;  afterwards  sailed  by 
the  following  log  account: 

LOG-BOOK  OR  SLATE-TABLE. 


02 

OJ 

CC 

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CO 

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£2 

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to 

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0 

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^ 

noon 

20 

0 

SSE.      r 

eparti 

ire. 

low 

0  30  W. 

S.  33  00  E. 

SNh«^ 

1 

6 

5 

SE.  by  E. 

NE. 

1  pt. 

9 

3  40  E. 

S.  51  20  E. 

+=>  no  O  e3  O 

Cg  tq  j-.   Q 

2 

5 

0 

t  b 

it 

** 

it 

S.  51  20  E. 

3 

6 

0 

SE. 

ENE. 

2pt. 

9 

2  00  E. 

S.  30  30  E. 

X^  5.S  ~^' 

4 

5 

5 

ESE. 

S. 

>t 

9 

4  30  E. 

S.  28  00  E. 

"S  r  =-  s  ®  ** 

5 

5 

0 

E.  by  N. 

SSE. 

it 

9 

7  30  E. 

N.  53  45  E.  ,  t  =«  §  S=' 

6 

5 

0 

ft 

b  b 

it 

'' 

N.  53  45  E. 

S  S*H"S  S-  * 

7 

5 

0 

44 

tl 

" 

99 

1C 

N.  53  45  E. 

"^  x  cS       C 

8  P.M. 

5 
3 

0 
0 

NE. 
Current 

SE. 
,  true  £ 

1  pt. 
>W. 

8  00  E. 

N.  31  45  E. 
S.  45  00  W. 

"tiSl 

In  this  case  the  opposite  point  to  the  bearing  of  the  light- 
house NNW.  is  SSE.,  which  enter  as  the  first  course  and  the 
distance  20  miles  as  the  first  distance.  The  variation  supposed 
to  be  found  on  the  chart  was  10°  W..  and  from  the  deviation 
table  for  the  course  SSE.  we  find  00°  30'  W.,  which,  applied 
to  the  left  as  they  are  both  westerly,  gives  the  true  course 
S.  33°  00'  E. 

Again,  for  the  second  course  at  1  P.M.  the  log  indicated  the 
ship  as  making  5  miles  the  first  hour  and  the  compass  course 
SE.  by  E.  with  the  wind  NE.  or  on  the  port  tack,  the  leftside; 
hence  the  leeway  of  one  point  is  to  the  right.  The  variation 


SIMPLE   ELEMENTS   OF    NAVIGATION. 


of  10  degrees  is  west  or  left,  and  the  deviation  from  the  table 
3°  40'  is  east  or  right;  hence  the  true  course  is  S.  51°  20'  E.  in 
the  last  column,  and  so  on  with  the  other  courses. 

The  drift  of  the  current  being  one  and  a  half  miles  per  hour 
for  the  last  two  hours  drove  the  ship  3  miles  in  the  direction  of 
the  set  SW.  true,  which  enter  as  though  the  ship  had  sailed 
that  the  last  course  and  distance. 

Having  now  obtained  the  true  courses  sailed,  enter  them  in 
the  table  of  the  working-book  with  the  sum  of  the  distances 
made  on  each  course: 


WORK-TABLE. 


DIPP.  LATITUDE. 

DEPARTURE. 

Courses. 

Distances. 

N. 

S. 

E. 

W. 

0          / 

S.  33  00  E. 

20.0 

16.8 

10.9 

S.  51  20  E. 

11.5 

7.2 

8.9 

S.  30  30  E. 

6.0 

5.2 

3.0 

S.  28  00  E. 

5.5 

4.8 

2.5 

N.  53  45  E. 

15.0 

8.8 

12.1 

N.  31  45  E. 

5.0 

4.2 

2.6 

S.  45  00  W. 

3.0 

2.1 

2.1 

13.0 

36.1 

40.0 

2.1 

13.0 

2.1 

Diff.  Lat.        23.1 

37.9      Departure. 

Course  made  good  S.  58°  E.   and  distance  made  good  44 
miles. 

Lat.  Cape  Henry  Light  36°  55'  05"  N.    Long,         76°  00'  02"  W. 
Difference  of  latitude         23'  06"  S.    Diff.  Long.       47'  00"  E. 


Latitude  in    .     . 

Sum  of  latitudes 
Middle  latitude 


.  36°  31'  59"  K   Long,  in    75°  13'  02"  W. 

.  73°  27'  04" 

.  36°  43  30"  or  36|". 


The  first  course,  33°,  is  found  at  the  top  of  the  page  of  Table  I, 
and  opposite  to  the  distance  of  20  the  Lat.  column  gives  16.8 
and  the  Dep.  column  gives  10.9,  which  place  in  their  appro- 
priate column  in  the  work-table;  the  difference  latitude  under 
S.  and  the  departure  under  E.  as  the  ship  has  sailed  south  and 


DEAD-BECKONING. 


east.  Do  the  same  way  with  each  course  to  the  nearest  degree 
is  sufficient. 

After  adding  up  the  different  columns  it  will  be  seen  there 
were  more  southings  than  northings,  and  their  difference  will 
give  23.1  S.  as  the  difference  of  latitude  made  good.  There 
are  more  eastings  than  westings,  and  their  difference  will  give 
37.9  E.,  the  departure  made  good. 

In  Table  I  the  place  where  these  come  nearest  in  their 
respective  columns  is  opposite  44  in  the  distance  column,  which 
is  the  distance  made  good. 

The  departure  being  greater  than  the  difference  of  latitude, 
the  course  made  good  is  found  at  the  bottom  of  the  page, 
S.  58"  E. 

The  latitude  of  Cape  Henry  being  north  and  the  difference 
of  latitude  made  good  being  south  \ve  take  their  difference  and 
get  the  latitude  in  36°  31'  59 "  K,  the  name  of  the  greater. 

With  the  middle  latitude  36|  as  a  course  in  Table  I,  the  de- 
parture made  good  is  found  in  the  Lat.  column  opposite  the 
distance  47,  which  is  the  difference  of  longitude  cf  the  same 
name  as  the  departure,  which  is  east,  and  as  the  longitude  of 
Cape  Henry  is  west  we  take  their  difference  to  find  the  longi- 
tude in  75°  13'  02"  W.,  the  name  of  the  greater. 

From  this  new  position  of  the  ship  the  bearing  and  distance 
of  the  designated  place  are  again  found,  and  the  new  course 
followed  as  nearly  as  possible. 

From  8  P.M.,  the  time  of  the  last  position,  the  ship  sailed  on 
a  course  by  compass  ESE.,  with  the  wind  free,  100  miles  per 
log  until  8  A.M.  the  following  morning;  the  chart  showing  2 
points  easterly  variation  and  a  constant  drift  of  2  miles  per 
hour  in  a  true  SW.  direction.  Find  the  position  again.  In 
this  case  there  would  not  be  any  leeway. 

LOG-TABLE. 


Hours. 

Knots. 

Courses. 

Wind. 

Lee. 

Var. 

Dev. 

True 
courses. 

12 

100 
24 

ESE. 
Set  of 

NW. 

the  cur 

0 
rent 

2  pts.  E. 
SW.  true. 

4°  30'  E. 

SE.  M  S. 
SW. 

The  variation  2  points  being  easterly  and  the  deviation  from 
the  table  4°  30'  E.  or  nearly  |  point  easterly,  both  are  applied 
to  the  right  to  get  the  true  course. 


30 


SIMPLE   ELEMENTS   OF   NAVIGATION. 


WORK-TABLE. 


Courses. 

Distance. 

DIFF.  LATITUDE. 

DEPARTURE. 

N. 

S. 

E. 

W. 

0        1       II 

S.  39  22  30  E. 
S.  45  00  00  W. 

100 
24 

77.3 
17.0 

63.4 

17.0 

94.3 

63.4 
17.0 

17.0 

Diff.  Lat.       94.3 

46  4    Departure. 

Course  made  good  S.  26°  E.,  and  105  miles  the  distance  made 
good. 

In  this  case,  the  nearest  the  difference  of  latitude  and  de- 
parture came  together  in  their  appropriate  columns  in  Table 
I.  was  opposite  to  105,  the  distance  made  good.  As  the  de- 
parture was  less  than  the  difference  of  latitude  the  course 
S.  26°  E.  or  SSE.  i  E.  was  found  on  top  of  the  page  as  the 
course  made  good. 

Latitude  of  last  position    36°  31'  59"  N. 
Difference  of  Latitude  .       1°  34'  18"  S. 


Latitude  in  ... 
Sum  of  the  Latitudes 
Middle  Latitude  . 


34°  57'  41"  N. 

71°  29'  40". 

35°  44'  50"  or  35f". 

With  this  middle,  latitude  35f,  enter  Table  I,  and  find  de- 
parture in  the  Lat.  column,  and  opposite  to  it  in  the  distance 
column  is  57  miles,  the  difference  of  longitude  of  the  same 
name  as  the  departure,  which  is  east. 

Longitude  of  the  last  position    75°  13'  02"  W. 
Difference  of  longitude      .     .  57'          E. 


Longitude  in    .     ...     .     74°  16'  02"  W. 

At  noon  of  that  day  the  ship  was  found  by  the  log  to  have 
sailed  30  miles  NE.  by  E.  close  to  the  wind  on  the  starboard 
tack  or  right  hand,  making  two  points  leeway.  Variation  by 
the  chart  7°  30'  W. 

From  the  deviation  table  the  deviation  on  a  NE.  by  E.  course 
is  8°  10'  E.  The  leewav  will  be  to  the  left. 


DEAD-RECKOXING. 


31 


Compass  course  NE.  by  E.  is  N.  56°  15'  00"  E. 
Deviation  E 8'  10"  to  the  right. 

Magnetic  course  N 64°  15'  00"  E. 

Variation  W 7'  30"  to  the  left. 

True  course  N 56°  45'  00"  E. 

Or  nearly  N.  57°  E. 

WORK-TABLE. 


Courses. 

Distance. 

DIFF.  LATITUDE. 

DEPARTURE. 

N. 

S. 

E. 

W. 

N.  57  E. 

30 

16.3 

25.2 

16.3 

25.2 

16.3       Diff.  Lat. 

25.2    Departure. 

Course  made  good  N.  57°  E.,  and  30  miles  the  distance  made 
good. 

With   the  middle  latitude  35 
and   the  departure  25.2  in  the 
Lat.  column,   the    difference  of 
longitude  is  found  to  be: 
Diff.  longitude         31'  00"  E. 
Longitude  left  74°  16'  02"  W. 
Longitude  in     73°  45'  02"  W. 
From  this  position  the  ship  sailed  from  day  to  day  on  the 
following  courses  and  distances,  taken  from  the  log-book  and 
stated  in  the  following  table: 

LOG-BOOK. 


Lat. 
Diff. 

Lat. 
Sum 
Mid. 

left 
Lat. 

in 

of  Lats. 
Lat. 

34° 

57' 
16' 

41" 
18" 

N. 

35° 

70° 
35° 

13' 
11' 
05' 

59" 
40" 
50" 

N. 

Courses. 

Distances. 

13 
S 

a 

*J3 

J 

03 

<D 

Q 

True 

courses. 

ENE. 
E  byN. 

E  byS. 
E. 
SE. 
ENE. 

30 

40 
80 
60 
30  E 
5J  C 

N. 
NNE. 

rift 

2 
2  4 

0      / 

15  SOW. 
10  10W. 
500E. 
700  E. 
...700E. 

0         / 

7  20  E. 
7  30  E. 
5  50  E. 
6  40  E. 
2  00  E. 

0          / 

N.  73  33  45  E. 
S.  81  35  00  E. 
S.  48  14  00  E. 
S.  53  50  00  E. 
S.  36  00  00  E. 
N.  67  30  00  E. 

urrent,  true  coui 

"se 

REMARKS.— The  ship  drifted  during  the  time  in  a  gale  by  wind  and  sea 
30  miles  SE.  by  compass.    By  current  marked  in  chart  ENE.  50  miles, 


32 


SIMPLE    ELEMENTS    OF    NAVIGATION. 


In  the  second  course  it  will  be  seen  that  after  variation  and 
deviation  and  leeway  are  applied,  the  course  is  greater  than 
90  degrees,  or  we  have  gone  through  E.  from  the  north  and 
have  come  nearer  S.  than  N. ;  therefore  we  subtract  from  180 
degrees,  which  gives  the  true  course  S.  81°  35  E.  from  the 
South. 

WORK-TABLE. 


Courses. 

Distances. 

DIFP.  LATITUDE. 

DEPARTURE. 

N. 

S. 

E. 

W. 

0           / 

N.  73  34  E. 
S.  81  35  E. 
S.  48  14  E. 
S.  53  50  E. 
S.  36  00  E. 
N.  67  30  E. 

30 
40 
80 
60 
30 

8.6 
19.1 

6.0 
53.3 
35.3 
24.3 

28.7 
39.5 
59.7 
48.5 
17.6 
46.2 

27.7 

118.9 
27.7 

240.2 

Diff  .  Lat.       91.2 

240.2    Departure. 

Course  made  good  S.  69°  E.  and  257  miles  made  good. 
With  the  first  course  enter  Table  I  with  the  course  73. 
On  page  with  73  at  the  bottom  and  opposite  to  30  in  the  dis- 
stance  column  will  be  found  in  the  Lat.  column  8.8,  and  on 
page  with  74  r.t  the  bottom  and  opposite  to  30  in  the  distance 
column  will  be  found  in  the  Lat.  column  8.3,  making  a  differ- 
ence of  .5  for  one  degree  in  the  course:  hence  for  half  a  degree 
it  will  be  one  half  of  .5,  or  .2,  to  be  subtracted  from  8.8  in  the 
first  case,  which  will  give  8.6  for  the  difference  of  latitude  for 
the  first  course,  which  place  in  the  column  N.  as  northings. 
As  there  is  so  little  difference  between  the  departure  for  73  and 
74,  that  for  either  course  may  be  used  as  the  departure  in  its 
appropriate  column  under  E.,  and  so  on  in  each  course. 

With  middle  latitude  34^  and 
the  departure  240.2  in  the  Lat. 
column,  the  difference  of  longi- 
tude is  found  to  be  291.5  in  the 
distance  column;  divide  by  60 
and  we  get : 

Diff.  longitude    4°  51'  30"  E. 
Longitude  left   73°  45'  02"  W. 
Longitude  in  .  68°  53'  32"  W, 


Lat. 
Diff. 

Lat. 
Sum 
Mid. 

left 
Lat. 

in 

of  Lats. 
Lat. 

35° 
1° 

13' 
11' 

59" 
12" 

N. 
S. 

34° 
69° 
34° 

02' 
16' 

38' 

42" 
46" 
23" 

N. 

DEAD-RECKONING.  33 

Continue  in  this  way  until  the  port  is  reached. 
If  it  is  not  convenient  to  find  the  course  and  distance  on  the 
chart  with  the  parallel  rulers  and  dividers,  it  may  be  done  in  the 
following  manner.  Suppose,  for  instance,  it  is  desired  to  know 
the  compass  bearing  and  distance  from  the  last  position  back 
to  Cape  Henry. 

Lat.  of  Cape  Henry  36°  55'  05"  N. 
Lat.  of  last  position  34°  02'  47"  N. 

Diff.  Latitude    2°  52'  18" 
60 


120 
52 

172.3 

Long,  of  Cape  Henry  76°  00'  02"  W. 
Long,  last  place  68°  53'  32"  W. 


Diff.  Longitude  7°  06'  30" 
60 


426.5 
Sum  of  Latitudes  70°  57'  52" 

Middle  Latitude  35°  28'  56"  or 
The  difference  of  longitude  is  too  great  for  the  distance 
column  in  the  table,  so  divide  it  by  2  for  convenience,  and  with 
the  half  of  the  longitude,  213.2,  enter  Table  I,  and  opposite  to  it 
in  the  distance  column  for  35  and  36  will  be  found  174.5  and 
172  3  in  the  latitude  column;  the  middle  latitude  being  nearly 
35^,  take  the  mean  of  these,  173.4,  for  the  departure,  which 
multiplied  by  2  gives  346.8  for  the  whole  departure.  The 
whole  departure  and  difference  of  latitude  are  too  large  for  the 
table,  so  divide  by  any  convenient  number,  say  10,  which  gives 
17.2  diff.  latitude  and  34.7  departure;  with  these  seek  in  Table 
I  till  they  nearly  agree  on  a  course  S.  63°  W.  and  a  distance 
of  39.  Multiply  this  distance  by  10,  and  we  get  390  miles  as 
the  whole  distance. 

Hence  Cape  Henry  bears  true  S.  63°  W.,  distance  390  miles; 
and  to  get  the  compass  bearing  or  course,  variation  and  devia- 
tion must  be  applied.     Let  variation  be  16°  20'  W. 
True  course  S.  63°  00'  W. 
Variation  W.  16°  20'  apply  to  the  right. 


34  SIMPLE   ELEMENTS   OF   KAVIGATION. 

Magnetic  course  S.  79°  20'  W. 

Deviation  W.  8°  00'  to  the  nearest  point  to  the  right. 

Compass  course  S.  87°  20'  W. 

Or  the  ship  will  have  to  steer  S.   87°  20'  W.  390  miles  to 
return  to  Cape  Henry. 

Ship's  Track.  It  is  customary,  whenever  the  position  of 
the  ship  is  plotted,  to  draw  a  line  on  the  chart  from  that  posi- 
tion to  the  former  one,  and  the  lines  so  drawn  from  day  to  day 
will  be  the  ship's  track — a  distinction  from  the  traverse  which 
the  ship  makes  in  her  zigzag  course  sailing  from  one  position 
to  another  against  a  head  wind. 

EXAMPLES. 

I.  Required  the  compass  course  and  distance  from  latitude 
51°  25'  N.  and  longitude  9°  29'  W.,  to  latitude  49°  16  N.  and 
longitude  9°  29'  W.     The  variation  is  19°  20'  W.  and  deviation 
is  3°  16'  E. 

Ans.  Compass  course  S.  16°  04'  W.     Distance  129 
miles. 

II.  A  ship  sails  from  latitude  44°  30'  N.  290  miles,  when  she 
finds  her  departure  is  161.1.     What  is  the  true  course  she  has 
sailed,  the  difference  of  latitude,  and  latitude  in? 

Ans.  Course  NW.  by  N.     Diff.  latitude  241.1  and 
Latitude  in  48°  31'  06"  N. 

III.  What  is  the  position  of  the  ship  after  sailing  on  the 
following  courses  (true)  and  distances:  NNE.  40  miles;  E.  by 
S.  60  miles;  SE.  70  miles;  and  SW.  48  miles? 

Ans.  Diff.  lat.   58.2;  dep.  897;  course  made  good 
S.  57°  01'  E.;  distance  106.9. 

IV.  A  rock  was  sighted  in  latitude  39°  40'  S.,  longitude 
87°   15'  E.,  bearing  NNE.,    distant    15   miles.      Afterwards 
sailed:  E.  by  S.,  37  miles;  EKE.,  44  miles;  N.  £  W.,  51  miles; 
and  ESE.,  29  miles.     What  is  the  position  of  the  ship?   (The 
bearings  and  courses  are  true.) 

Ans.  Course  made  good  N.  70°  E. ;  distance  102 
miles.     Latitude  in  39°  05'  S.;  longitude  in  89°  17' E. 

V.  From  latitude  18°  35'  S.,  longitude  123°  23'  E.,  the  ship 
sails  225  miles  SW.  i  W.  by  compass.     What  is  her  position  ? 
The  variation  is  U  point  E.  and  deviation  is  6°  35'  W. 

Am.  Latitude  in  20°  24'  06"  S.;  longitude  in  119 
55'  00"  E. 


BY    OBSERVATIONS.  35 


VI.  A  danger  bears  by  compass  S.  34  E.  29  miles,  variation 
is  one  point  west,  and  deviation  is  1°  50'  E.  What  is  the  true 
bearing  of  the  danger  ?  The  latitude  of  the  danger  is  00°  52'  N. 
and  longitude  is  &  40'  E. 

Ans.  N.  43°  25'  W.,  29  miles. 


CHAPTER  IV. 
BY  OBSERVATIONS. 

THE  method  of  finding  the  ship's  position  by  dead-reckon- 
ing must  of  course  be  liable  to  many  errors,  arising  from  the 
great  difficulty  in  steering  a  steady  course,  different  rates  of 
sailing  between  the  times  of  heaving  the  log,  incorrect  allow- 
ance for  leeway  and  variation,  and  more  frequently  from  the 
effects  of  the  drift  of  the  sea  and  unknown  currents  ;  hence  it 
becomes  necessary  to  determine  the  position  by  celestial  ob- 
servations when  the  opportunity  offers. 

The  Zenith.  The  heavens  appear  to  form  the  upper  half 
of  a  hollow  sphere,  and  this  celestial  surface  may  be  conceived 
to  be  divided  by  imaginary  circles  that  are  made  to  correspond 
with  those  of  the  earth  ;  thus  if  the  axis  of  the  earth  were  ex- 
tended it  would  p-.iss  through  the  north  and  south  poles  of  the 
heavens.  The  celestial  equator  is  a  circle  in  the  heavens  cor- 
responding with  the  equator  of  the  earth,  and  the  celestial 
meridians  correspond  also  with  those  of  the  earth  ;  hence  it 
will  be  seen  that  if  we  determine  the  point  immediately  over 
head,  called  The  Zenith,  it  would  be  the  same  as  finding  the 
position  of  the  ship  on  the  earth.  The  method  for  finding 
this  position  differs  from  that  of  dead-reckoning  in  the  de- 
termination of  the  position  directly  from  observations  of  the 
heavenly  bodies  and  not  by  a  reference  to  some  other  geo- 
graphical spot. 

The  instruments  used  to  obtain  the  data  necessary  for  the 
determination  of  the  position  by  observations  are  the  Chro- 
nometer and  Sextant. 

The  Chronometer  is  a  superior  kind  of  watch,  so  con- 
structed that  its  daily  gain  or  loss  by  variation  of  temperature 


36  SIMPLE    ELEMENTS   OF   NAVIGATION". 

is  reduced  to  a  minimum.  The  machinery  is  of  such  delicate 
construction  that  the  greatest  possible  care  must  be  taken  of 
it  both  at  sea  and  in  harbor.  It  should  never  be  moved  from 
its  place  on  board,  but  kept  as  near  the  same  temperature  as 
possible,  and  is  defended  from  violent  shocks  by  the  case^being 
lined  with  soft  wool  and  preserved  in  a  horizontal  position  by 
being  hung  on  gimbals.  It  should  be  wound  up  every  day  at 
the  same  hour  and  the  key  turned  steadily  through  each  turn. 

Error  and  Rate.  The  chronometers  are  intended  to  keep 
the  mean  time  of  Greenwich,  but  as  none  of  these  are  perfect 
the  Error  should  be  ascertained  before  going  to  sea  and  also 
its  Daily  Rate. 

The  error  is  said  to  be  fast  or  slow  as  the  chronometer  is  fast 
or  slow  of  Greenwich  mean  time.  The  daily  rate  is  the 
change  in  its  error  in  twenty-four  hours,  and  if  the  instrument 
is  going  too  fast  the  rate  is  said  to  be  gaming:  if  too  slow, 
losing. 

A  chronometer  is  best  rated  at  an  observatory ;  but  at  all 
large  sea-ports  an  electrical  ball  is  dropped  at  a  certain  hour 
every  day  from  a  point  at  which  it  can  be  seen  from  all  over 
the  harbor.  By  a  comparison  with  this  the  error  can  be  found, 
and  if  taken  in  successive  days  the  rate.  In  the  absence  of 
this  some  good  clock-maker  can  be  found  to  compare  your 
chronometer  with  one  of  known  rate  and  error. 

After  going  to  sea  the  rate  is  almost  sure  to  change  some; 
and  it  is  not  unwise,  on  arriving  in  port,  to  compare  with  the 
chronometers  of  other  ships,  should  there  be  no  time-ball.  The 
difference  between  the  two  rates  being  divided  by  the  interval 
elapsed  will  be  what  is  called  the  sea  rate. 

The  Sextant  is  an  instrument  used  to  measure  the  altitude 
of  a  heavenly  body  above  the  horizon,  or  the  angular  distance 
between  objects.  The  description,  names,  and  uses  of  the  dif- 
ferent parts  may  be  best  learned  from  the  instrument  itself, 
which  may  be  found  in  almost  any  optician's  store. 

From  the  figure  the  names  of  the  different  parts  maybe  seen. 
AA  is  the  limb  ;  7,  the  index -bar  ;  M,  the  index-glass,  which 
stands  upon  and  moves  with  the  index-bar ;  m  is  the  horizon- 
glass  fixed  to  the  frame,  and  which  is  only  silvered  on  half  the 
surface;  Pand  Q  are  the  shade-glasses  to  modify  the  bright- 
ness of  the  sun  ;  E  is  the  sight -tube  or  telescope  carried  by  the 
collar  .5!" ;  H  is  the  magnifying-glass  to  assist  in  reading  the 


BY   OBSERVATIONS. 


37 


scale,  is  attached  to  an  arm  which  moves  upon  a  pivot  S ;  B 
is  the  tangent-screw  to  give  a  small  motion  to  the  index-bar 


THE  SEXTANT. 

when  the  clamp-screw  is  tight,     C  is  the  clamping-screw,  and 
Fis  the  vernier  carried  by  the  index-bar. 

The  limb  is  graduated  to  120°  from  the  zero  point  and 
to  a  few  degrees  on  the  opposite  side  of  the  zero  point.  The 
degrees  are  divided  at  every  ten  or  twenty  minutes,  and  these 
are  subdivided  by  the  vernier  to  ten  or  twenty  seconds,  thus 
enabling  the  angles  to  be  read  by  estimating  to  five  or  ten 
seconds. 

The  Adjustments  are  four  in  number.  I.  See  if  the  in- 
dex-glass is  perpendicular  to  the  plane  of  the  instrument  by 
placing  the  index  near  the  middle  of  the  limb,  and  whilst 
looking  in  the  index-glass  see  if  the  reflected  limb  in  the  glass 
forms  an  unbroken  line  with  the  limb  itself  ;  if  not,  make  it  so 
by  means  of  the  screws  at  the  back  of  the  glass. 

II.  See  if  the  horizon-glass  is  perpendicular  to  the  plane  of 
the  instrument,  by  looking  through  the  sight-tube  and  the 
horizon-glass  at  the  horizon  and  holding  the  instrument  in  a 


38  SIMPLE   ELEMENTS   OF   KAVIGATIOK. 

vertical  position,  move  the  index  till  the  reflection  of  the 
horizon  in  the  silvered  part  of  the  glass  forms  an  unbroken 
line  with  the  one  seen  direct,  fasten  the  index  by  the  clanlp- 
screw  and  incline  the  instrument  to  the  right  or  left  to  see 
whether  the  true  and  reflected  horizons  continue  to  form  an 
unbroken  line ;  if  not,  they  can  be  made  so  by  means  of  the 
screw  at  the  back  of  the  instrument. 

III.  See  that  the  axis  of  the  telescope,  when  screwed  into 
the  collar,  is  parallel  to  the  plane  of  the  instrument  by  placing 
two  of  the  wires  of  the  telescope  parallel  to  the  plane  of  the 
instrument,  and  then  measure  the  distance  between  two  objects 
more  than  90°  apart,  and  bring  them  in  contact  on  the  wire 
nearest  the  instrument;  by  moving  the  sextant  slightly  the  two 
objects  may  be  brought  to  the  other  wire  ;   if  they  still  be  in 
contact  the  adjustment  is  correct,  but  if  they  separate  or  top 
one  over  the  other,  the  adjustment  is  made  by  means  of  the 
screws  in  the  collar  of  the  telescope. 

IV.  See  that  the  horizon-glass  is  parallel  to  the  index-glass 
when  the  zero  of  the  vernier  is  opposite  to  zero  on  the  limb 
by  looking  at  the  horizon  and  holding  the  instrument  in  a 
vertical   position.     Place   the   two   zeros   together  and   look 
through  the  horizon  glass  at  the  horizon,  holding  the  instru- 
ment vertical.     If  the  true  horizon  through  the  clear  part  of 
the  glass  appear  in  a  straight  line  with  the  reflected  in  the 
silvered  part  the  two  glasses  are  parallel  ;  if  not  they  are  made 
so  by  turning  the  lower  screw  at  the  back  of  the  glass. 

Index  Error.  If  this  last  adjustment  has  not  been  cor- 
rectly made  the  instrument  can  be  used  as  well,  but  the  read- 
ing will  want  correction  for  every  angle  measured  ;  this  cor- 
rection is  called  the  Index  Error.  This  error  is  found  by  mak- 
ing the  horizons  form  an  unbroken  line  whilst  holding  the  in- 
strument in  a  vertical  position,  and  the  distance  from  zero  on 
the  limb  to  the  zero  on  the  vernier  will  be  the  index  error,  to 
be  subtracted  from  the  angles  measured  if  zero  on  the  vernier 
is  to  the  left  of  zero  on  the  limb,  otherwise  add.  A  more  ac- 
curate way  is  by  measuring  the  diameter  of  the  sun  on  both 
sides  of  zero.  If  both  measurements  read  alike  there  will  be 
no  index  error ;  if  they  are  unlike,  half  their  difference  will 
be  the  index  error,  to  be  subtracted  if  the  measurement  taken 
on  the  left  of  zero  is  larger  ;  otherwise,  to  be  added. 

To  Take  an  Altitude.     When  taking  an  altitude  of  the  sun 


UY   OBSERVATIONS.  39 

it  is  customary  to  bring  the  sun's  lower  limb  in  contact  with 
the  horizon,  but  if  the  lower  limb  is  obscured  the  upper  limb 
can  be  used.  As  no  level  or  plumb-line  can  be  used  in  taking 
the  altitude  the  sextant  should  be  held  as  nearly  perpendicular 
as  possible,  and  when  the  reflected  image  is  brought  down  to 
the  horizon  by  moving  the  index  by  hand  clamp  it  there,  ancT 
while  sweeping  the  horizon  the  image  will  appear  to  form  a 
curve  ;  use  the  tangent-screw  till  the  limb  just  touches  the 
horizon  at  the  lowest  part  of  the  curve. 

The  altitude  when  thus  taken  on  the  meridian  enables  us  to 
find  the  latitude,  and  when  not  taken  on  the  meridian  fur- 
nishes the  means  of  finding  the  time  of  the  ship  and  thence 
the  longitude.  This  altitude  above  the  sea  horizon  is  called 
the  Apparent  Altitude  and  must  be  corrected  to  reduce  it  to 
the  True  Altitude.  These  corrections  are  :  dip,  index  error, 
refraction,  parallax,  and  semi-diameter. 

The  Dip  is  the  depression  of  the  sea  horizon  below  the  level 
of  the  eye,  and  will  depend  upon  the  elevation  of  the  e}'e  above 
the  level  of  the  sea  ;  should  be  subtracted  from  the  apparent 
altitude  because  it  makes  the  altitude  appear  more  than  it 
really  is.  The  dip  is  given  in  Table  II. 

Refraction  is  due  to  the  earth's  atmosphere,  which  bends 
the  rays  of  light  passing  through  it  into  a  position  more  nearly 
vertical  and  thus  enabling  us  to  see  a  heavenly  body  when 
really  belowr  the  horizon.  The  effect  then  of  refraction  is  to 
make  the  heavenly  body  appear  higher  than  it  really  is  ;  hence 
the  correction  for  refraction  must  be  substracted  from  the 
apparent  altitude.  This  correction  depends  upon  the  altitude 
of  the  heavenly  body  being  most  when  near  the  horizon  and 
nothing  when  in  the  zenith.  The  refraction  is  given  in 
Table  II. 

Parallax  is  a  correction  to  be  added  to  the  apparent  alti- 
tude to  make  it  what  it  would  have  been  if  observed  at  the 
centre  of  the  earth.  The  parallax  decreases  with  the  altitude, 
being  most  when  in  the  horizon  and  nothing  when  in  the 
zenith.  Parallax  is  given  in  Table  II. 

Semi-diameter  is  the  correction  to  be  applied  to  obtain  the 
altitude  of  the  centre  of  the  object.  If  the  lower  limb  of  the 
sun  was  used  it  should  be  added  to  the  apparent  altitude  and 
subtracted  when  the  upper  limb  is  used.  The  semi  diameter  of 
the  sun  may  be  taken  at  16'. 


40  SIMPLE   ELEMENTS   OF   NAVIGATION. 


CHAPTER  V. 
To  FIND  THE  LATITUDE. 

Astronomical  Date.  In  finding  certain  data  from  the 
tables  the  astronomical  date  is  used,  which  begins  12  hours 
behind  the  civil  date,  and  is  counted  from  noon  to  noon,  or  24 
hours,  whereas  the  civil  date  commences  at  midnight  and  is 
divided  into  two  parts  of  12  hours.  Suppose  the  day  is  what  is 
ordinarily  called  the  4th  July,  and  it  wants  2  hours  to  noon,  it 
would  be  10  A  M.  of  the  4th  July  civil  date,  but  astronomi- 
cally it  is  July  3d,  22  hours. 

To  Find  the  Latitude.  The  latitude  of  a  place,  being  its 
distance  from  the  equator  measured  on  the  meridian,  must 
correspond  with  the  distance  from  the  celestial  equator  to  the 
zenith.  As  the  zenith  is  right  overhead,  it  is  90  degrees  from 
the  horizon  ;  hence,  if  the  celestial  equator  were  visible  in  the 
heavens,  it  would  only  be  necessary  to  take  its  altitude,  which 
subtracted  from  90  would  give  the  latitude.  As  we  cannot  see 
the  equator,  some  heavenly  body  is  taken  whose  distance  from 
the  equator  is  known.  In  case  of  the  sun,  it  appears  to  move 
during  the  year  in  a  path  inclined  to  the  equator  at  an  angle  of 
23  degrees  and  28  minutes,  crossing  the  equator  twice  during 
the  year,  once  in  March  and  again  in  September,  reaching  its 
farthest  north  in  June  and  farthest  south  in  December.  Its 
distance  at  any  time  from  the  equator  measured  on  a  meridian 
is  called  its  Declination,  -north  when  it  is  north  of  the  equator, 
and  south  wJien  south  of  it. 

The  declination  is  given  in  Table  III  for  each  month  when 
the  sun  is  on  the  meridian  of  Greenwich;  and  as  the  declina- 
tion is  constantly  changing,  the  difference  for  one  hour  is  also 
given  in  the  table. 

To  find  the  declination  at  any  time,  obtain  the  astronomical 
date,  and  take  from  Table  III  the  declination  opposite  the  day 
of  the  mouth  ;  now  multiply  the  difference  for  one  hour  by 
the  longitude  in  time,  which  is  one  hour  for  every  15  degrees, 
and,  if  the  declination  be  increasing,  add  in  west  but  subtract 
in  east  longitude.  If  the  declination  be  decreasing,  subtract 
in  west  but  add  in  east  longitude. 


TO    FIND   THE   LATITUDE.  41 

The  Meridian  Altitude  of  the  sun  is  the  greatest  it  will 
acquire  during  the  day,  and  as  it  crosses  the  meridian  it  is 
necessary  to  commence  taking  its  altitude  a  little  before,  and 
keep  its  image  in  contact  with  the  horizon  till  it  begins  to 
fall.  Correct  this  altitude  to  find  the  true  altitude  accord- 
ing to  the  principles  previously  explained,  and  to  avoid  any 
mistakes  it  would  be  best  to  prefix  the  signs  of  addition  and 
subtraction,  +  and  — ,  to  the  known  corrections  and  those  that 
are  found  in  Table  II.  These  corrections  may  be  written  in  a 
separate  form,  and  applied  one  to  the  other  according  to  their 
several  signs  for  a  whole  correction  to  be  added  or  subtracted 
as  the  sign  implies. 

Meridian  Zenith  Distance.  As  the  zenith  is  90  degrees 
from  the  horizon,  subtracting  this  true  meridian  altitude  from 
90  will  give  the  distance  of  the  sun  from  the  zenith  while  on 
the  meridian,  or  the  meridian  zenith  distance.  This  meridian 
distance  mark  north  when  the  sun  bears  south,  or  south  when  it 
bears  nwth. 

Now  with  the  meridian  zenith  distance  given  and  the  decli- 
nation known,  the  latitude  is  found  by  adding  them  together 
if  they  are  of  the  same  name,  or  taking  their  difference  if  of 
different  names.  The  latitude  will  be  of  the  same  name  as 
the  greater. 

EXAMPLES. 

At  sea,  June  21,  1887,  in  longitude  60°  W.,  the  observed 
altitude  of  the  sun's  lower  limb  was  40°  04'  ;  sun  bearing 
south  ;  index  correction  3'  00"  (add) ;  height  of  the  eye  20 
feet.  Find  the  latitude. 

In  Table  III,  with  the  year  at  the  top  and  the  clay  of  the 
month  at  the  left  of  the  page,  we  find  the  declination  under 
June  to  be  23°  27'  N.,  and  the  corresponding  difference  for 
one  hour  to  be  zero.  This  difference  for  one  hour  multiplied 
by  four  hours,  the  longitude  (60  divided  by  15),  gives  for  the 
correction  to  the  declination  nothing  ;  hence  the  true  declina- 
tion is  23°  27'  00"  N. 

The  observed  altitude,  40°  04',  having  been  corrected  as  be- 
fore explained,  the  true  altitude  is  found  to  be  40°  17'  35", 
which  subtracted  from  90  gives  the  meridian  zenith  distance 
49°  42'  25",  which  is  marked  north  as  the  sun  bore  south. 

The  declination  and  meridian  zenith  distance  having  the 


42  SIMPLE   ELEMENTS   OF   KATIGATIOK1. 

same  name,  we  take  their  sum  and  find  the  latitude  to  be 
72°  09'  25"  N. 

For  the  sake  of  convenience  it  is  always  best  to  have  a  par- 
ticular.form  for  all  problems  in  which  the  data  are  written  and 
the  result  obtained  ;  besides  it  tends  to  preserve  neatness  in 
the  navigation  book,  and  facilitates  an  easy  means  of  compari- 
son with  other  results. 

The  form  in  this  case  should  be: 

Obs.  Alt.  40°  04'  00"  S.  D.  +16'  00" 

Corr.   +13  35  I.   C.  +   3  00 

Ref .  -     1  09 

True  Alt.  40  17  35  Dip         4  23 

90  00  00  Par.  +       07 

M.  Z.  D.  49  42  25  N.  Cor.  +  13  35 

True  Dec.  23  27  00  N. 


Latitude  7j  09  25  K 

Dec.  23°  27'  00"  N.          Hr.  Diff.  0" 
Corr.        00  00  Long.  4  hrs. 


True  Dec.  23    27  00  N.  Corr.  0 

At  sea  June  1,  1886,  in  longitude  44°  40'  W.,  the  observed 
altitude  of  the  sun's  lower  lirnb  was  72°  14'  10";  sun  bearing 
south;  index  error  +  3'  45";  height  of  the  eye  22  feet.  Find 
the  latitude. 

Longitude  44°  40'  W.  is  3  hrs.  14  m.  40  s.  W.,  or  34  hrs 
nearly. 

Obs.  Alt.  72°  14'  10"  S.  D.  +  16'  00" 

Corr.   +  14  54  I.  C.  +  3  45 

Ref.          0  1$ 

True  Alt.  72  29  04  Dip          4  36 

90  00  00  Par.    +         3 


M.  Z.  D.  17   30   56    N.  Corr.  + 14  54 

True  Dec.  22  06  £g    K. 


Latitude   39   3£  ®t   N.  6  ; 

Dec.  22°  05'  00"  N.  Hr.  Diff.  20" 

Corr.  +105  Long.  3|  hrs 


True  Dec.  22  06  05    K  Corr.  +6©'  or+1'  05' 


TO    F1XD    THE    LATITt'DK.  43 

At  sea  June  25,  1886,  in  longitude  59°  15'  E.  (3  h.  57  min.), 
the  observed  altitude  of  the  sun's  upper  limb  was  60°  23'  14"; 
sun  bearing  north;  index  error  --  2'  21";  height  of  the  eye  30 
feet.  Find  the  latitude. 

Obs.  Alt.  60°  23'  14"  S.  D.  -  16'  00" 

Corr.      -  24   12  I.  C.  -      2  21 

Ref.  -  33 

True  Alt.  59   59  02  Dip          5  22 

90  00  00  Par.  -f          4 
M.  Z.  D.  30  00  58  S. 

True  Dec.  23  24   15.8  N.  Corr.  -24    12 


Latitude     6  36  42.2  S. 

Dec.  23°  24'  00"  N.  Hr.  Diff.  4" 

Corr.  15.8  Long.  3.95  hrs. 


True  Dec.  23  24   15.8  N.  Corr. +15". 80 

At  sea  October  3,  1887,  in  longitude  67°  30'  W.,  the  observed 
meridian  altitude  of  the  sun's  lower  limb  was  40°  23'  50  ';  sun 
bearing  N.;  index  correction  Jr  1'  30';  height  of  the  eye  18 
feet.  Find  the  latitude. 

Obs.  Alt.  40°  23'  50"  S.  D.  +  16'  00' 

Corr.    +  12  20  I.  C.  +   1    30 

Ref.  -      1   07 

True  Alt.  40  36   10  Dip         4  11 

90  00  00  Par.  -f        08 


M.  Z.  D.  49   23   50  S.  Corr.  -f  12  20 

True  Dec.    4  00  21  S. 


Latitude    53  24'  11  S. 

Dec.  3°  56'  00"  S.  Hr.  Diff.       58" 

Corr.  -|-    4  21  Long.       4.5  hrs. 


True  Dec.  4  00  21  S.  290 

232 


261"0 
Corr. +  4' 21" 

At  sea  Feb.   21,  1888,  in  longitude  45°  W.,  the  observed 
meridian  altitude  of  the  sun's  lower  limb  was,  55°  43'  10";  sun 


44  SIMPLE   ELEMENTS   OF   NAVIGATION". 

bearing  S.;  index  correction  —  2'  10";  height  of  the  eye  19 
feet.     Find  the  latitude. 

Obs.  Alt.  55°  43'  10"  S.  D.  +  16'  00" 

Corr.     -f   8   59  I.  C.  -  2  10 

Ref.  -       40 

True  Alt.  55  52  09  Dip  4  16 
90  00  00  Par.  +  5 


M.  Z.  D.  34  07  51  N.  Corr.  +  8  59 

True  Dec.  10  35  18  S. 


Latitude    23  32  33  N. 

Dec.  10°  38'  00"  S.  Hr.  Diff.  54" 

Corr.    -    2  42  Long.    3  hrs. 


True  Dec.  10  35  18  S.  162" 

Corr.  -  2'  42" 

At  sea  Jan.  23,  1888,  in  longitude  4  hours  and  12  minutes 
E. ,  the  observed  meridian  altitude  of  the  sun's  lower  lirnb  was 
77°  15'  30";  sun  bearing  K;  index  correction  —  3'  10";  height 
of  the  eye  19  feet.  Find  the  latitude. 

Obs.  Alt.  77°  15'  30"  S.  D.  -f  16'  00" 

Corr.   +    8  23  I.  C.        3  10 

Ref.  -      0  13 

True  Alt.  77  23  53  Dip         4  16 

90  00  00  Par.  +   0  02 


M.  Z.  D.  12   36  07  S.  Corr.  -f   8  23 

True  Dec.  19  32  27  S. 


Latitude     32  08  27  S. 

Dec.  19°  30'  00  S.  Hr.  Diff.   35" 

Corr.   -f   2  27.  Long.  4. 2  hrs. 

True  Dec.  19  32  27  S.  70 

170 

147".0 

Corr.  •+ 2' 27" 

At  sea  April  20,  1888,  in  longitude  about  40°  15'  W.,  the 
observed  meridian  altitude  of  the  sun's  lower  limb  was  63° 


TO    FIND    THE    LONGDITUDE.  45 

01'  30";  sun  bearing  N. ;  index  correction  --  3'  10";  height  of 
the  eye  19  feet.    Find  the  latitude. 

Ohs.  Alt.  63°  01'  30"  S.  D.  + 16'  00" 

Corr.    -f    8   09  I.  C.  -      3   10 

Ref.  -     0  29 

True  Alt.  63   09  39  Dip         4   16 

90  00  00  Par.  +   0  04 


M.  Z.  D.  26  50  21  S.  Corr.  -f   8   09 

True  Dec.  11   48   18  N. 


Latitude    15  02   03  S. 

Dec.  11°  46'  00"  N.  Hr.  Diff.    51" 

Corr.      +  2  18  Long.  2.7  hrs. 


True  Dec.  11      48  18  N.  137".7 

Corr.  +  2'  17". 7 


CHAPTER  VI. 
To  FIND  THE  LONGITUDE. 

THE  earth  in  its  revolution  about  its  axes  from  west  to  east 
once  in  twenty-four  hours  causes  the  sun  to  pass  over  360 
degrees  in  that  time,  which  is  equal  to  15  degrees  per  hour. 
As  longitude  is  measured  on  the  equator  in  degrees,  minutes, 
and  seconds,  we  have  at  once  the  connection  between  it  and 
time,  or  15°  is  equivalent  to  one  hour,  15'  to  one  minute,  and 
15"  to  one  second.  As  the  motion  of  the  sun  is  from  east  to 
west,  apparently,  it  follows  that  all  places  east  of  us  will  have 
the  sun  on  their  meridian  before  it  comes  to  ours,  therefore 
it  will  be  later  there  than  at  our  place  ;  and  all  places  to  the 
westward  of  us  will  have  the  sun  on  their  meridian  after  it 
has  passed  ours,  therefore  it  will  be  earlier  there  than  at  our 
place.  Now,  it  has  been  stated,  the  first  meridian,  from  which 
all  longitudes  are  reckoned,  is  the  one  passing  over  Green- 
wich ;  hence  the  difference  of  time  between  Greenwich  and 
any  place  is  the  longitude  of  that  place.  To  find  the  longi- 
tude, then,  of  any  place  would  be  to  find  the  time  of  the  place 
and  apply  it  to  the  Greenwich  time. 


46  SIMPLE    ELEMENTS    OF    NAVIGATION. 

As  the  sun,  which  is  supposed  to  mark  the  days  and  hours 
by  its  passage  in  the  heavens,  is  irregular  in  its  motion,  it  is 
necessary  to  take  into  consideration,  besides  the  two  modes  of 
counting  dates,  two  kinds  of  time — apparent  time  and  mean 
time. 

Apparent  Time  is  that  shown  by  the  sun,  estimating  the 
apparent  noon  the  moment  the  sun  passes  the  meridian,  and  if 
it  were  possible  to  determine  that  moment  with  accuracy  at 
sea,  we  could  then  obtain  the  apparent  time  at  ship  ;  but  the 
length  of  the  days  would  vary  as  much  as  half  an  hour  during 
the  year  if  they  were  determined  by  the  sun's  passage  over 
the  meridian. 

Mean  Time.  As  it  is  impossible  to  construct  watches  or 
chronometers  to  show  this  apparent  time,  we  make  use  of 
what  is  called  mean  time,  which  makes  the  days  of  uniform 
length  throughout  the  year,  and  is  therefore  sometimes  in 
advance  of  the  time  shown  by  the  sun  and  sometimes  behind 
it.  This  is  the  time  shown  by  all  well-regulated  watches  and 
chronometers. 

Equation  of  Time.  There  is  sometimes  a  difference  of  a 
quarter  of  an  hour  between  this  apparent  and  mean  time. 
This  difference  is  called  the  equation  of  time,  and  is  given  in 
Table  IV  at  Greenwich  noon  for  each  day  of  the  month,  and 
must  be  applied  to  the  apparent  time  according  to  the  instruc- 
tions given  at  the  top  of  the  column,  in  order  to  obtain  the 
mean  time.  This  equation  of  time  found  in  Table  IV  must 
be  corrected  for  the  Greenwich  time.  In  Table  IV«,  under 
the  daily  variation  at  the  top  and  opposite  the  hour  of  Green- 
wich at  the  side,  the  number  of  seconds  will  be  found  to 
aPPty  to  the  equation  of  time  found  in  Table  IV  to  obtain 
the  correct  equation  of  time. 

The  method  of  obtaining  the  apparent  time  at  sea,  and  thence 
the  mean  time,  is  by  observing  the  altitude  of  the  sun,  taken 
either  in  the  forenoon  or  afternoon  when  it  is  rising  or  falling 
fastest,  or  when  bearing  nearly  east  or  west,  noting  the  time 
by  watch  at  the  same  instant. 

The  preliminary  steps  in  solving  this  problem  will  consist 
in  finding  the  following  data:  the  correct  Greenwich  date  ex- 
pressed astronomically,  the  true  altitude  of  the  sun,  latitude  of 
the  place,  and  the  polar  distance  of  the  sun. 

The  Greenwich  date  is  found  by  comparing  the  watch  with 


TO   FIND   THE    LONGITUDE.  47 

the  chronometer,  which  will  give  the  time  shown  by  the  chro- 
nometer when  the  observation  was  taken  ;  apply  the  error 
and  rate  of  the  chronometer  and  the  Greenwich  mean  time  is 
obtained. 

The  true  altitude  is  found  by  correcting  the  observed  alti- 
tude for  semi  diameter,  index  correction,  refraction,  clip,  and 
parallax  in  the  same  manner  as  explained  for  correcting  the 
meridian  altitude. 

The  latitude  of  the  place  is  found  by  dead-reckoning  from 
the  last  position  to  the  time  of  observing  the  altitude.  It  is 
sometimes  the  practice  to  observe  an  altitude  in  the  morning 
for  time  and  delay  working  till  noon,  when  the  meridian  alti- 
tude gives  the  latitude  which  is  worked  back  by  dead-reckon- 
ing to  the  time  of  taking  the  observation. 

The  polar  distance  is  the  distance  of  the  sun  from  the  north 
pole  when  the  observation  is  taken  in  north  latitude,  and  its 
distance  from  the  south  pole  when  taken  in  south  latitude. 

Take  from  Table  III  the  declination  corresponding  to  the 
Greenwich  date,  and  multiply  the  difference  for  one  hour  by 
the  Greenwich  time,  which  apply  as  before  explained  to  obtain 
the  true  declination. 

As  the  declination  is  the  distance  of  the  sun  from  the  equator 
and  the  equator  is  90°  from  the  poles,  it  follows  that  the  declina- 
tion subtracted  from  90  if  of  the  same  name  [as  the  latitude, 
or  added  if  of  a  contrary  name,  will  give  the  polar  distance. 

Having  thus  found  the  correct  altitude,  latitude,  and  polar 
distance,  the  apparent  time  of  observation  may  be  found  by 
the  following  method  and  the  use  of  Table  V.  In  this  table, 
if  the  sine  or  cosine  sought  is  marked  at  the  top  of  the  page, 
the  title,  hour  A.M.  or  P.M.,  is  also  found  at  the  top,  and  the 
contrary  if  the  sine  or  cosine  is  marked  at  the  bottom. 

Add  together  the  altitude,  latitutie,  and  polar  distance  and 
take  half  their  sum  ;  from  this  half  sum  subtract  the  altitude 
and  note  the  remainder.  Take  from  Table  V  the  secant  of 
the  latitude,  the  cosecant  of  the  polar  distance  (rejecting  10 
in  the  index),  the  cosine  of  the  half  sum,  and  the  sine  of  the 
remainder  ;  add  these  together  and  take  half  the  sum,  which 
seek  for  in  the  column  of  sines,  and  opposite  to  it  will  be  the 
corresponding  apparent  time. 

Take  from  Table  IV  the  equation  of  time  corresponding  to 
the  Greenwich  date,  corrected  for  Greenwich  time  by  Table 


48  SIMPLE   ELEMENTS   OF   NAVIGATION. 


and  apply  it  to  this  apparent  time  according  to  the 
directions  at  the  top  of  the  column,  and  we  shall  obtain  the 
mean  time  of  the  observation.  Take  the  difference  between 
this  and  the  Greenwich  time,  and  the  result  is  the  longitude 
east  when  the  Greenwich  time  is  the  least,  and  west  if  the 
Greenwich  time  is  greater  than  the  time  of  the  place. 

EXAMPLE. 

On  Nov.  9,  1889,  in  the  forenoon,  the  observed  altitude  of 
the  sun's  lower  limb  was  22°  29'  20"  ;  height  of  the  eye  17 
feet;  index  correction  -f-  2'  45";  watch  time  of  observation 
8h  51m  57s  A.M.;  slow  of  chronometer  time  4h  54m  158 ;  chro- 
nometer correction  —  2m  12s ;  with  latitude  by  dead-reckoning 
35°  North.  Find  the  longitude. 

PREPAKATION   OF   DATA. 

W.  Time  8"  51m  57s  A.M.   Obs.  Alt.  22°  -29'  20" 
C.— W.  4  54  15          S.  D.  +  16  00 

I.  C.  +  2  45 

C.  Time  1   46    12  P.M.  Ref.    -    2  20 

C.  Corr.    -  2    12  Dip   -    4  02 

Par.   +         8 


G.  M.  T.  1   44    00  P.M. 


True  Alt,  22   41  51 

Dec.    17°  00'  00"  S.  DiflE.  lb  43" 

Corr.       -f   1  13  G.  M.  T.     1.7 


True  Dec.    17   01  13    S.  Corr.   73.1 

90   00  00  or  -f  1'  13" 


Pol.  Dist.  107   01  13 

SOLUTION. 

Alt.    22°  41'  51" 

Lat.    35   00  00  sec      0.08664 

Pol.  Dist.  107   01  13  cosec      0.01945 


Sum  164   43  04 


Half  Sum    82   21  32  cos     9.12374 

Alt.    22   41  51 


Rem.    59   39  41  sin      9.93604 

2)19.16587 
sin      9.58293 


TO    FIXD    THE    LONGITUDE.  49 


Local  App.  Time  8h  59m  589  A.M. 
Equation  of  Time      -  16    01 

Local  M.  Time  8   43    57  A.M. 

Gr.  M.  Time  1    44    00  P.M. 


Diff.  Time    5   00    03 
Longitude  75°  00'  45"  W. 

Equation  of  Time,  Table  IV,  •     16m  028 

Daily  Variation  6s 
Correction,  Table  IVa,  —  1 


Equation  of  Time  16  01 

About  8  A.M.  April  3,  1888,  in  latitude  20°  45'  S.  and  east 
longitude,  the  observed  altitude  of  the  sun's  lower  limb  was 
24°  37'  10"  ;  index  correction  -|-  2'  20"  ;  height  of  the  eye  19 
feet ;  watch  time  of  observation  7h  57m  07s. 5  ;  slow  of  chro- 
nometer time  51'  57m  24s  ;  chronometer  correction  —  3m  388. 
Find  the  longitude. 

PREPARATION   OF   DATA. 

W.  Time    7h  57m  07s. 5  Obs.  Alt,  24°  37'  10" 

C.— W.    5    57    24  S.  D.   -f  16  00 

I.  C.   +    2  20 

C.  Time    1    54    31.5  Ref.          2  06 

C.  Corr.        -  3    38  Dip  4  16 

Par.    +    0  08 


G.  M.  T.  3d  13   50    53.5 


True  Alt,  24   49  16 


Dec.    5°  35'  00"  N.  Hr.  Diff.  57" 

Corr.    +  13  06  G.  M.  T.  13.8  hrs. 


True  Dec.    5   48  06    K  786.6 

90   00  00  Corr.  -f  13'  06". 6 


Pol.  Dist.  95   48  06 

SOLUTION. 

Alt.    24°  49'  16" 

Lat.    20   45  00  sec  0.02913 

Pol.  Dist.    95   48  06  cosec  0.00223 


Sum  141    22  22 


50  SIMPLE   ELEMENTS   OF   NAVIGATION. 

Half  Sum    70   41  11  cos     9.51948 

Alt.    24   49  16 


Rem.    45    51  55  sin      9.85594 

2)19.40678 

Local  App.  Time  7h  57m  17s  A.M.  sin      9.70339 

Equation  of  Time   +  3    00 


Local  M.  Time  8   00    17  A.M. 
Gr.  M.  Time  1    50    53.5  A.M. 


Diff.  Time  6   09    23.5 
Longitude  92°  20'  33"  E. 

Equation  of  Time,  Table  IV,  +  3m  10» 

Daily  Variation  18s. 
Correction,  Table  IV«,  —        10 

Equation  of  Time  +  3    00 

About  8  A.M.  Feb.  21,  1888,  in  latitude  24°  10'  N.  and 
west  longitude,  the  observed  altitude  of  the  sun's  lower  limb 
was  21°  44'  10";  index  correction  --  2'  10";  height  of  the  eye 
19  feet ;  watch  time  of  observation  8h  Olm  12s ;  slow  of  chro- 
nometer time  3h  04m  07s ;  chronometer  correction  -{-  7m  35s. 
Find  the  longitude. 

PREPARATION  OF  DATA. 

W.  Time    8"  01'"  12s  A.M.        Obs.  Alt.  21°  44'  10" 
C.— W.    3   04    07  S.  D.   +  16  00 

I.  C.          2  10 

C.  Time  11    05    19  A.M.  Ref.  -      2  25 

C.  Corr.    -f    7    35  Dip         4  16 

Par.  +    0  08 

G.  M.  T.  22d  23   12    54  


or  True  Alt.  21    51  27 

21st  --  0».79 

Dec.  10°  38'  00"  S.         Hr.  Diff.       54" 
Corr.  +  43  G.  M.  T.  -  79 


True  Dec.    10   38  43    S.  Corr.  -f  42.66 

90   00  00 


Pol.  Dist.  100   38  43 


TO    FIND    THE    LONGITUDE. 


51 


SOLUTION. 

Alt.    21°  51'  27" 
Lat.    24   10  00 
Pol.  Dist.  100   38  43 


sec 
cosec 


0.03983 
0.00754 


Sum  146    40  10 


Half  Sum    73   20  05 
Alt.    21    51  27 


Rem.    51    28  38 

Local  App.  Time  7h  59m  53s  A.M. 
Equation  of  Time  +13    53 


cos     9.45754 


sin      9.89340 

2)19.39831 

sin     9.69915 


Local  M.  Time   8   13    46  A.M. 
Gr.  M.  Time  11    12    54  A.M. 


Diff.  Time    2   59    08 
Longitude  44°  47'   00"  W. 

Equation  of  Time,  Table  IV,  -f  13m  53s 

Daily  Variation  O8. 
Correction,  Table  IV«,  0 

Equation  of  Time  -f  13    53 

On  April  3,  1888,  in  the  forenoon,  in  latitude  29°  42'  30"  S. 
and  east  longitude,  the  observed  altitude  of  the  sun's  lower 
limb  was  22°  41'  30"  ;  index  correction  -  -  2'  30"  ;  height  of 
the  eye  24  feet;  watch  time  of  observation  8h  06m  20s. 5  ; 
slow  of  chronometer  time  8h  08m  14s ;  chronometer  correction 
-  6m  19s.  Find  the  longitude. 

PREPARATION   OF   DATA. 


W.  Time    8h  06m  20s. 5  A.M. 

C  W.    8   08    14 


C.  Time    4   14    34  .5 
C.  Corr.      -  6    19 


G.  M.  T.  2d  16  08  15.5 
or 

3d  -  7h.86. 


Obs.  Alt,  22°  41'  30" 
S.  D.  +  16  00 
I.  C.  2  30 
Ref.  2  19 
Dip  -  4  48 
Par.  -f  08 


True  Alt.  22  48  01 


SIMPLE    ELEMENTS    OF    NAVIGATION. 


Dec.    5°  35'  00"  N. 
Corr.      -  7  28 


Hr.  Diff.      57" 
G.  M.  T.  -  7.86 


True  Dec.    5   27  32    N. 
90   00  00 


Corr.  448.02 
or 

-  7'  28" 


Pol.  Dist.  95  27  32 

SOLUTION. 

Alt.    22°  48'  01" 
Lat.    29  42  30 
Pol.  Dist.    95   27  32 


sec 
cosec 


0.06120 
0.00198 


Sum  147   58  03 


Half  Sum    73    59  01 

Alt.    22   48  01 


Rem.  51    11  00 

Local  App.  Time  8h  00m  43s  A.M. 
Equation  Time    -f  3    15 


cos     9.44077 


sin     9.89162 

2)19.39557 

sin      9.69778 


Local  M.  Time  8   03    58  A.M. 
Gr.  M.  Time  4   08    15.5A.M. 


Diff.  Time  3   55    42.5 
Longitude  58°  55'  37"  E. 

Equation  of  Time,  Table  IV,  +  3m  10s 

Daily  Variation  18s. 
Correction  Table  YVa,         -{-  5 


Equation  of  Time  -f  33  15 


CHAPTER  VII. 


IT  has  already  been  said  the  sun  should  be  observed  for 
time  when  bearing  nearly  east  or  west,  for  then  the  altitude 
cannot  only  be  observed  with  more  accuracy  and  the  time 
npted  more  exactly  when  the  sun  is  rising  or  falling  the  fast- 


A    SUMNER.  53 

est,  but  the  longitude  can  be  found  without  the  necessity  of 
the  latitude  being  accurately  known;  in  fact  an  uncertainty 
of  two  or  three  degrees  in  the  latitude  would  not  make  much 
difference  in  the  time  derived  from  the  observation. 

As  the  sun  begins  to  move  away  from  the  east  or  west 
points  the  error  in  the  latitude  begins  to  affect  the  longitude 
more  and  more,  until  at  north  or  south  a  very  slight  difference 
in  the  latitude  makes  a  great  difference  in  the  longitude. 

The  sun  can  only  pass  the  east  or  west  points  when  its  dec- 
lination is  of  the  same  name  as  the  latitude;  but  when  they 
are  of  contrary  names  the  sun  cannot  bear  east  or  west,  but 
will  come  nearer  to  those  points  at  rising  or  setting,  at  \vhich 
time  the  low  altitude  is  too  much  affected  by  the  excessive 
refraction.  In  either  case  clouds  and  other  causes  will  often 
interfere  to  prevent  the  observation  being  taken  at  or  near 
the  proper  bearing;  hence  it  is  plain  the  latitude  should  be 
accurately  known. 

Now  it  will  often  happen  that  a  meridian  altitude  for  lati- 
tude cannot  be  had  for  several  days,  while  at  the  same  time 
dead-reckoning  must  be  relied  upon  to  work  the  latitude  up 
to  the  time  of  the  observation,  from  which  an  error  is  sure  to 
follow.  It  remains,  then,  to  show  what  use  can  be  made  of 
the  sun  to  find  the  position  of  the  ship  when  the  sun  occupies 
a  place  neither  east  nor  west  nor  on  the  meridian.  This 
brings  us  now  to  the  most  important  problem  in  navigation, 
and  one  which  is  universally  used  at  sea,  called  "  a  simmer." 

This  method  consists  in  working  the  observation,  when 
the  latitude  is  uncertain,  with  two  assumed  latitudes,  the  one 
a  little  greater  and  the  other  a  little  less  than  the  latitude  we 
are  supposed  to  be  in,  by  which  one  observation  for  time  en- 
ables us  to  find  the  bearing  of  laud,  and  two  observations,  be- 
tween which  the  sun  has  changed  its  bearing,  will  give  us 
both  the  latitude  and  longitude  provided  the  chronometer  is 
right  or  its  error  and  rate  are  known. 

Circles  of  Equal  Altitudes.  At  any  given  instant  the 
sun  is  vertically  above  some  point  on  the  earth's  surface.  At 
this  spot  an  observer  with  a  sextant  would  find  the  true  alti- 
tude of  the  sun's  centre  to  be  90  degrees.  If,  however,  the  ob- 
server should  shift  his  position  away  from  the  sun,  its  dis- 
tance from  his  zenith  would  of  course  become  greater  and  its 
altitude  less.  He  would  then  be  situated  upon  a  small  circle 


54  SIMPLE   ELEMENTS   OF   NAVIGATION. 

the  centre  of  which  would  be  the  spot  under  the  sun.  All 
persons  on  that  circle  would  have  the  sun  at  an  equal  alti- 
tude. Finally,  when  he  came  to  the  horizon,  all  points  on  the 
circle  would  have  the  sun  in  the  horizon.  These  circles  of 
equal  altitudes  cut  the  various  parallels  of  latitude  and  merid- 
ians at  different  angles.  Near  the  east  and  west  points  the 
circles  runup  and  down  nearly  with  the  meridians;  so  that 
if  the  observer  were  at  the  east  or  west  points  of  the  circle  it 
would  make  little  difference  whether  the  latitude  were  exact 
or  not,  for  there  the  longitude  remains  nearly  the  same  for  a 
long  distance  in  latitude.  Near  the  north  and  south  points 
the  circles  run  nearly  east  and  west  with  the  parallels  of  lati- 
tude; so  that  if  he  were  at  one  of  those  points  of  the  circle,  a 
very  slight  difference  in  the  latitude  would  make  a  great  dif- 
ference in  the  longitude.  Hence  it  follows  if  an  observer 
had  a  certain  altitude  we  see  that  different  latitudes  would 
put  him  at  different  points  of  his  circle  of  equal  altitudes, 
and  that  these  points  would  differ  in  longitude,  at  first  slowly 
when  near  east  or  west,  and  then  more  rapidly  as  the  point 
approached  north  or  south. 

Line  of  Position.  As  the  circles  are  so  large,  compared 
with  the  difference  between  the  latitudes  which  are  used,  this 
portion  of  the  circle  may  be  regarded  as  a  straight  line,  which 
line  is  called  a  line  of  position,  and  is  always  at  right  angles 
to  the  bearing  of  the  sun. 

To  obtain  this  line  of  position  in  actual  practice,  assume  a 
latitude  which  is  10  to  30  minutes  greater  than  that  by  dead- 
reckoning  and  a  latitude  10  to  30  minutes  less,  and  from  each 
of  these  work  out  the  observation  for  time.  From  the  two  re- 
sulting longitudes  and  the  latitude  of  each,  plot  the  positions 
on  the  chart  and  connect  them  by  a  straight  line;  we  shall 
then  have  a  line  on  which  the  ship  is  somewhere. 

If  this  line  runs  parallel  to  the  coast,  its  distance  is  approxi- 
mately known,  and  the  bearing  of  some  known  point  on  shore 
or  a  cast  of  the  lead  will  give  the  position  on  the  line.  If  the 
line  on  the  chart  be  extended  till  it  meets  a  point  of  land,  it 
shows  the  bearing  of  that  point.  Although  the  exact  distance 
of  this  point  is  unknown,  yet  we  have  only  to  sail  on  this  line 
till  the  point  is  reached.  Thus  it  is  seen  how  with  one  obser- 
vation the  ship  may  be  kept  out  of  the  danger  whose  bearing 
or  distance  is  not  exactly  known. 


A   SUMMER.  65 

If,  after  the  sun  has  changed  its  bearing  not  less  than  three 
points, — but  the  nearer  to  eight  points  the  better, — we  should 
take  another  observation,  it  will  give,  by  working  in  the  same 
manner,  a  second  line  of  position,  which  must  cross  the  first 
one  at  some  point,  as  they  are  each  at  right  angles  to  the  sun 
at  the  moment  of  observation.  If  the  ship  has  not  changed 
her  position  between  the  observations,  the  point  of  intersection 
of  the  two  lines  of  position  will  be  the  position  of  the  ship, 
But  in  practice  the  ship  is  very  seldom  stationary  between  the 
observations,  and  to  find  her  position  at  the  moment  of  the 
last  one,  lay  off  on  the  chart  from  the  first  line  of  position  the 
course  and  distance  made  good  between  the  two  observations, 
and  draw  a  parallel  line  to  this  first  line  of  position;  then  the 
ship  would  be  somewhere  on  the  parallel  line  after  having 
sailed  a  certain  distance  in  a  given  direction.  As  the  ship  is 
also  on  the  second  line  of  position,  its  intersection  with  the 
parallel  line  will  be  the  position  of  the  ship  at  the  moment  of 
taking  the  second  observation. 

If  the  two  lines  of  position  do  not  intersect,  the  latitudes 
used  were  not  far  enough  apart,  and  the  lines  must  be  pro- 
longed till  they  do  meet. 

EXAMPLES. 

On  Nov.  9,  1889,  in  the  forenoon,  in  latitude  34°  40'  N.  by 
dead-reckoning,  observed  the  altitude  of  the  sun's  lower  limb 
22°  29'  20";  watch  time  of  observation  8h  51m  57s  A.M.,  slow 
of  chronometer  time  4h  54m  15s;  chronometer  correction  —  2m 
128;  height  of  the  eye  17  feet;  index  correction  -\-  2 °  45'.  Find 
the  line  of  position.  Assume  the  latitudes  34°  10'  and  35°  10' 
N. 

PREPARATION    OF   DATA. 

W.  Time  8"  51m  57s  A.M.  Obs.  Alt.  22°  29'  20" 

C.— W.  4  54    15  S.  D.    -f  16  00 

I.  C.    +2  45 

C.  Time  1  46  12  P.M.          Ref.    2  20 
C.  Corr.  -   2  12  Dip  —  4  02 

Par.  -f    8 
Gr.  M.T.I  44  00  P.M.      True  Alt.  22  41  51 

Dec.   17°  00'  00"  S.  Diff.  1  hr.  43" 

Corr.        -f  1    13  G.  M.  T.  1.7 


56  SIMPLE    ELEMENTS   OF   NAVIGATION. 

True  Dec.    17    01   13    S.  Corr.  73". 1 

90  00  00  or       1'  13" 


Pol.  Dist.  107  01   13 

SOLUTION. 

Alt.    22°  41'  51" 

Lat.    34  10  00  sec    0.08228 

Pol.  Dist.  107  01  13  cosec    0.01945 


Sum  163  53  04 


Half  Sum    81   56  32  cos    9.14669 

Alt.    22  41   51  sin    9.93417 


Rem.    59  14  41 


2)19.18259 


sin  9.59129 
Alt.    22°  41' 51" 

Lat.    35  10  00  sec  0.08752 

P.  D.  107  01   13  cosec  0.01945 


Sum  164  53   04 


Half  Sum    82  26  32  cos    9.11901 

Alt.    22  41   51 


Rem.    59  44  41  sin    9.93641 


2)19.16239 

sin    9.58119 

L.  A.  T.     8h  56™  168  L.  A.  T.  9h  00™  438 

Eq.  T.     -  16    01  Eq.  T.  -  16    01 


L.  M.  T.     8  40    15  A.M.  L.  M.  T.  8  44    42  A.M. 

G.  M.  T.      1  44    00  P.M.  G.  M.   T.  1   44    00  P.M. 


Diff.  T.     5  03   45  Diff.  T.  4  59    18 

or  or 

Longitude    75°  56'  15"  W.  Longitude  74°  49'  30"  W. 

Plot  these  two  positions  on  the  chart  and  connect  them  by 
a  straight  line  which  gives  a  line  of  position  AA,  and  if  the 


A   SUMNER. 


57 


observation  was  good  and  the  chronometer  right,  the  ship  is 
on  this  line  somewhere.  Although  the  exact  position  on  the 
line  is  not  known,  its  direction  affords  an  accurate  knowledge 
of  the  least  possible  distance  the  ship  can  be  from  the  point  of 
dan  tier  P. 


10 


?0    E 


20 


10 


75 


SO 


I   i   i  i   i  i    I   i   i    i   i   i   i   i   i   i   i   |   |   |   M   I   I   I  I   I   ii   I   I   I   I   I   I   I   I   I   I   I   II   I   I   II   II  TT~ 


40 


2G 


10 


35 


«> 


^0 


10 


35 


50 


40 


50 


40 


30 


40 


40 


After  determining  the  line  of  position  by  the  forenoon  ob- 
servation, the  ship  was  headed  due  north, but  at  noon  a  merid- 
ianaltitude  for  latitude  could  not  be  got,  and  the  latitude  by 
dead-reckoning  being  too  uncertain,  another  observation  was 
taken  about  4  P.M.,  the  ship  having  made  good  20  miles  in  the 
interval.  The  observed  altitude  of  the  sun's  lower  limb  was 
17°  44'  10";  watch  time  of  observation  4!l  04m  538  P.M.,  slow  of 


58  SIMPLE    ELEMENTS   OF   NAVIGATION. 

chronometer  time  4h  12in  20s;  chronometer  correction  —  2m  12s; 
height  of  the  eye  17  feet;  index  correction  -f-  2'  45".  Find 
the  second  line  of  position  and  the  position  of  the  ship.  The 
latitude  by  dead-reckoning  being  35°  N,(  assume  the  latitudes 
34°  30'  and  35°  30'  N. 

PREPARATION   OF  DATA. 

W.  Time  4h  04m  53s  Obs.  Alt.  17°  44'  10" 

C.— W.  4  12    20  S.  D.   +  16  00 

I.  C.    +    2  45 

C.  Time  8  17    13  P.M.  Ref.    -    3  01 

C.  Corr.    -  2    12  Dip   -    4  02 

Par.   -f        -8 


Gr.M.  T.  8  15    01  P.M. 


Tr.  Alt.  17  56  00 

Dec.   17°  00'  00"  S.  Diff.     1  hr.  43" 

Corr.   +  6  54  G.  M.  T.  8    25 


True  Dec.    17  06  54  S.  Corr.       354". 75 

90  00  00  +6'   54" 


Pol.  Dist.  107  06  54 

SOLUTION. 

Alt.    17°  56'  00" 

Lat,    34  30  00  sec    0.08401 

P.  D.  107  06  54  cosec    0.01968 


Sum  159   32  54 


Half  Sum    79  46  27  cos    9.24927 

Alt.     17  56  00 


Rem.    61   50  27  sin    9.94529 


2)19.29825 

sin    9.64912 

Alt.    17°  56'  00" 

Lat.    35  30  00  sec     0.08931 

P.  D.  107  06  54  cosec    0.01968 


Sum  160  32  54 


A   SUMKER.  59 

Half  Sum    80  16  27  cos    9.22737 

Alt.    17   56   00 


Rem.    62  20  27  sin    9.94730 


2)19.28366 

sin    9.64183 

L.  A.  T.  3h  31m  47s  L.  A.  T.      3"  28™  OO8 

Eq.  T.  - 16    01  Eq.  T.      -  16    01 


L.  M. 
G.M. 

T.  3 
T.  8 

15 
15 

46  P. 
01  P. 

M. 
M. 

L. 
G. 

M. 
M. 

T. 
T. 

3 

8 

11 
15 

59 

01 

P.M. 
P.M. 

Diff.  T.  4  59    15  Diff.  T.      5  03    02 

or  or 

Longitude  74°  48'  45"  W.         Longitude     75°  45'  30"  W. 

From  any  point  on  the  line  of  position  AA,  set  off  the  true 
course  north,  and  the  distance  20  miles  made  good  in  the  in- 
terval, and  through  the  spot  draw  the  parallel  line  BB.  Then 
plot  the  two  positions  by  the  P.M.  observation  on  the  chart, 
and  connect  them  by  a  straight  line  which  will  give  a  second 
line  of  position  CO.  The  point  D  where  it  cuts  the  parallel 
line  BB  will  be  the  position  of  the  ship  at  the  moment  of  the 
second  observation. 

Had  there  been  no  other  line  of  position,  CG  prolonged 
would  give  the  bearing  of  the  point  of  land  or  danger  P  •  and 
though  its  distance  would  not  be  accurately  known,  the 
soundings  might  give  it :  hence  the  danger  could  be  avoided 
by  shaping  a  course  in  a  direction  away  from  the  line  of  posi- 
tion. 

Should  it  be  intended  to  dodge  the  point  of  laud  and  make  a 
port  E  on  the  other  side,  draw  a  parallel  line  O'C'  to  CG 
through  E,  and  with  the  dividers  measure  the  shortest  dis- 
tance bb  between  OG  and  C'  C' ;  run  that  distance  on  a  course 
perpendicular  to  CG ;  then  by  changing  the  course  in  the  di- 
rection of  C'C'  the  vessel  will  make  the  port  bright  ahead. 

Had  it  been  possible  to  obtain  a  meridian  altitude  for  lati- 
tude, we  could  have  laid  off  from  the  first  line  of  position  the 
course  and  distance  made  good  from  the  time  of  observa- 
tion to  noon,  and  then  drawn  a  parallel  to  AA.  The  spot  where 


60  SIMPLE   ELEMENTS   OF   NAVIGATION. 

the  noon  latitude  cut  the  parallel  would  have  been  the  position 
of  the  ship  at  noon. 

It  will  be  seen  by  an  inspection  of  Table  V  that  the  cosine  of 
90  degrees  and  the  sine  of  zero  degrees  are  indeterminate; 
hence  the  nearer  the  half  sum  approaches  90  degrees  or  the 
remainder  zero,  the  more  indeterminate  or  uncertain  the  lon- 
gitude obtained  will  be. 

This  will  occur  when  the  sun  is  near  the  meridian.  Should 
the  half  sum  exceed  180  degrees,  or  be  less  than  the  latitude, 
the  assumed  latitudes  will  be  beyond  the  circle  of  equal  alti- 
tudes, and  other  latitudes  must  be  taken  nearer  the  one  that 
will  give  a  resulting  longitude! 


CHAPTER  VIII. 
ERROR  OF  THE  COMPASS. 

THE  error  to  which  the  compass  is  constantly  subjected, 
being  compounded  of  variation  and  deviation,  must  neces- 
sarily be  an  ever-changing  quantity.  In  some  localities  the 
variation  is  nearly  stationary,  but  in  others  there  is  an  annual 
change  more  than  likely  not  corrected  on  the  chart,  and  there 
are  parts  of  the  world  where  a  trifling  change  in  the  position 
of  the  ship  means  a  comparatively  large  change  in  the  amount 
of  the  variation.  The  deviation  table,  as  constructed  in  port, 
is  liable  to  many  changes  after  the  vessel  goes  to  sea.  It  is 
not  uncommon,  after  a  straight  run  for  several  days,  to  find 
the  deviation  change  fully  half  a  degree  for  every  degree  of 
alteration  in  the  compass  course,  and  in  some  instances  the 
compass  will  jump  a  point  or  two  without  an  alteration  of  the 
ship's  head.  This  is  due  to  a  change  of  heel,  loose  iron  placed 
near  the  compass,  boat  davits  turned  in  that  were  before 
swung  out,  or  the  many  causes  mentioned  in  the  first  chapter. 
From  this  it  will  be  seen  nothing  but  constant  watchfulness 
of  the  behavior  of  the  compass  can  ensure  safety;  to  this  end 
the  error  of  the  compass  is  frequently  determined. 

The  compass  bearing  of  the  sun  is  taken  and  the  true  bear- 
ing for  the  same  instant  is  calculated,  the  difference  between 


ERROR   OF   THE    COMPASS.  Gl 

the  two  being  the  error,  and  is  marked  E.  or  W.  according  as 
the  compass  bearing  falls  to  the  left  or  right  of  the  true  bear- 


ing. 


Should  the  error  be  found  to  change  much,  it  would  be  ad- 
visable to  head  the  vessel  so  as  to  get  the  error  on  every  few 
points  in  that  half  of  the  compass  most  likely  to  be  used  dur- 
ing the  next  few  days,  and  especially  so  if  approaching  land. 

There  are  three  ways  of  finding  the  true  bearing  of  the  sun 
at  sea  :  by  lines  of  position,  by  an  amplitude,  and  by  an  observed 
altitude. 

By  Line  of  Position.  The  most  simple  method  of  deter- 
mining the  true  bearing  of  the  sun  is  by  the  lines  of  position 
plotted  on  the  chart  and  sufficiently  accurate  for  all  purposes 
in  navigation. 

It  has  been  said  the  sun  always  bears  at  right  angles  to  the 
line  of  position  :  so  at  any  point  on  the  line  of  position  draw  a 
perpendicular  and  refer  it  to  the  true  compass  on  the  chart. 
The  direction  of  this  perpendicular  is  the  true  bearing  of  the 
sun;  comparing  this  with  the  compass  bearing  at  the  time  of 
taking  the  observation  from  which  the  line  of  position  was  de- 
rived, will  give  the  error. 

By  an  Amplitude.  When  the  sun  is  rising  or  setting,  its 
distance  from  the  E.  or  W.  points  of  the  horizon  is  called  its 
amplitude. 

As  refraction  causes  the  sun  to  appear  higher  than  it  actu- 
ally is,  and  its  effect  is  greatest  when  the  sun  is  in  the  horizon, 
being  about  equal  to  the  apparent  diameter  of  the  sun,  the 
bearing  should  not  be  taken  for  an  amplitude  when  the  cen- 
tre appears  in  the  horizon,  but  when  it  is  a  little  more  than  its 
diameter  plus  the  dip  above  the  horizon. 

Take  from  Table  III  the  declination  of  the  sun  for  the 
Greenwich  date  and  correct  it  for  the  Greenwich  time.  Add 
together  the  sine  of  the  declination  and  the  secant  of  the  lati- 
tude; from  Table  V  the  sum  (rejecting  10  in  the  index)  is  the 
sine  of  the  true  amplitude,  marked  E.  at  rising  and  W.  at  set- 
ting, and  N.  or  S.  as  the  declination  is  N.  or  S.  Should  the 
compass  amplitude  and  the  true  be  of  the  same  name,  their 
difference  will  be  the  error;  if  of  different  names,  their  sum 
will  be  the  error  for  the  course  the  ship  is  heading.  If  this 
error  be  to  the  right  of  the  variation  on  the  chart,  the  deviation 
will  be  easterly;  if  to  the  left,  westerly. 


62  SIMPLE    ELEMENTS    OF    NAVIGATION. 

EXAMPLE. 

At  sea  Nov.  27,  1887,  in  latitude  40°  27'  N. ,  longitude  20°  07' 
W.,  about  4h  43m  P.M.,  the  observed  bearing  of  the  sun  at  set- 
ting was  W.  17°  S. 

L.  M.  T.  4"  43m  P.M.  Dec.  21°  08'  S. 

Long.  1   20  W.  Corr.  -      2.42 


G.  M.  T.  6  03  P.M.    True  Dec.  21    05  18  S.      sin  9.55597 

Latitude40    27      N.     sec  0.11863 


sin  9.67460 

Diff.  1  hr.  27"  True  amplitude  W.  28°  13  S. 

G.  M.  T.  6h  Compass       "          W.  17         S. 

Corr.   -   162  or  2' 42"  

Error       11   13  W. 

If  the  variation  by  chart  was  10°  W.  the  deviation  would  be 
1°  13'  W.  for  the  point  of  the  ship's  head. 

By  an  Observed  Altitude.  At  the  time  of  taking  the  al- 
titude for  time  take  also  the  bearing  of  the  sun  by  compass, 
and  note  the  heading  of  the  ship;  also  the  heel,  and  whether  to 
port  or  starboard. 

The  preparation  of  the  data  in  this  problem  is  the  same  as 
that,  for  finding  the  time  by  observation,  and  it  is  usual  to 
combine  the  two.  To  find  the  true  bearing,  add  together  the 
true  altitude,  latitude,  and  the  polar  distance;  take  the  differ- 
ence between  the  half  sum  and  the  polar  distance,  and  note 
the  remainder.  Then  add  together  the  secant  of  the  altitude, 
secant  of  the  latitude  (rejecting  10  in  each  index),  cosine  of 
the  half  sum,  and  the  cosine  of  the  remainder;  half  the  sum 
of  the  four  quantities  will  be  the  cosine  of  half  the  true  bear- 
ing, which,  being  doubled,  will  give  the  true  bearing  reckoned 
from  the  north  in  north  latitude  and  the  south  in  south  lati- 
tude. 

EXAMPLES. 

We  will  take  the  first  example  used  in  finding  the  time, 
and  combine  the  two  problems  to  illustrate  the  form  used  in 
practice. 

PREPARATION   OF   DATA. 

W.  Time  8h  51m  57s  A.M.  Obs  Alt.  22°  29'  20" 

C.  -  -  W.  4   54    15  S.  D.  +  16  00 

I.  C.  -f-    2  45. 


ERROR   OF   THE    COMPASS.  63 

C.  Time  1    46    12  Ref.   -    2  20 

C.  Corr.       -  2     12  Dip         4   02 

Par.  + 8 

Gr.  M.  T.  1   44    00  P.M.         True  Alt.  22  41   51 

Dec.    17°  00'  00"  S.        Diff.  1  hr.  43" 
Corr.     -f     1  13  G.  M.  T.  1.7 


True  Dec.    17    01  13    S.        Corr.  731 
90    00  00  or  -f  1'  13" 


Pol.  Dis.  107    01  13 

SOLUTION. 

Alt.    22°  41 '51"  sec  0.03500 

Lat.    35   00  00  sec  0.08664  sec  0.08664 

Pol.  Dis.  107   01  13          cosec  0.01945 


Sum  164   43  04 


Half  Sum  82   21  32             cos  9.12374  cos  9.12374 
1st  Rem.  59    39  41              sin  9.93604 

2d  Rem.  24   39  41  cos  9.95846 

2)19.16587  2(19.20384 

sin  9.58293  cos  9.60192 

Local  App.  Time  8h  59m  58*  A.M.  Half  of  true  bearing  66°  26' 

2 


True  bearing  N.  132°  52'  E. 

Local  App.  Time  8h  59ra  58'  A.M.     True  bearing  N.  132°  52'  E. 
Equation  of  Time -16    01  Com.  bearing  N.  130   30  E. 

Local  M.  Time     8  43    57  A.M.     Com.  Error  2   22  E. 

Gr.  M.  T.     1   44    00  P.M. 


Diff.  Time     5  00    03 

or 
Longitude     75°  00'  45"  W. 

It  will  be  seen  from  the  above  example  that  as  it  requires 
very  little  more  work  in  the  solution  of  the  problem  for  time 
to  obtain  the  compass  error,  it  is  always  best  to  take  the 
bearing  of  the  sun  by  compass  at  the  same  instant  the  altitude 
is  taken  for  time  and  combine  the  two,  as  shown  in  examples. 

On  April  3,  1888,  in  the  forenoon,  in  latitude  29°  42'  30"  S. 
and  east  longitude,  the  observed  altitude  of  the  sun's  lower 


64: 


SIMPLE    ELEMENTS    OF    NAVIGATION. 


limb  was  22°  41'  30";  bearing  per  compass  S.  89°  E.;  index 
correction  —  2'  30";  height  of  the  eye  24  feet.  Watch  time  of 
observation  8h  06m  20s. 5;  slow  of  chronometer  time  8h  08m  14'; 
chronometer  correction -- 6m  19s.  Find  the  longitude  and 
error  of  the  compass. 

PREPARATION   OP  DATA. 

W.  Time  8h  06m  20S.5  A.M.          Obs.  Alt.  22°  41'  30" 
C.  -  -  W.  8   08    14  S.  D.   +  16  00 

I.  C.  2  30 

Ref.  2  19 

Dip  4  48 

Par.    -f         08 


C.  Time    4   14    34.5A.M. 
C.  Corr.      -  6    19 


G.M.T.2d  16   08    15.5 
or 

3d     -7h.86 

Dec.     5°  35'  00"  K 
Corr.       -7  28 


True  Alt.  22   48  01 


True  Dec.    5    27  32    K. 
90   00  00 


Hr.  Diff. 
G.  M.  T. 

Corr. 


Pol.  Dist.  95   27  32 

Alt.    22°  48'  01' 
Lat.    29   42  30 
Pol.  Dist.    95    27  32 


Sum  147    58  03 


Half  Sum  73  59  01 
IstRem.  51  11  00 
2d  Rem.  21  28  31 


SOLUTION. 

sec  0.06120 
cosec  0.00198 


cos  9.44077 
sin  9.89162 


57" 
-7.86 

448.02 
or 

-  7'  28" 


sec  0.03533 
sec  0.06120 


2)19.39557 
sin  9.69778 


cos  9.44077 

cos  9.96875 

2)19,50605 

cos  9.75302 


Local  App.  Time    8"  00m  43s  A.M. 
Equation  Time  -f-     3    15 


Local  M.  Time    8    03    58  A.M. 
Gr.  M.  Time    4    08    15  5  A.M. 


Diff.  Time    3    55    42.5 
Longitude  58^  55'   37"  E. 


CAUSES   THAT   AFFECT   XAVIGATIOX   AT   SEA.       05 

Eq.  Time  Table,  IV.,+3-"  10"  Half  of  true  bearing  55°  30'  37" 
Daily  Variation  18"  2 

Correction,  Table  IV a,  5 

True  bearing  S.  Ill  01  14  E. 
Equation  of  Time  -f-  3    15     Compass  bearing  S.    89  E. 


Compass  error   23  01  14  AV. 


CHAPTER  IX. 

CAUSES   THAT   AFFECT  NAVIGATION   AT   SEA. 

Clouds.  The  general  appearance  of  the  clouds  tends  greatly 
to  assist  the  navigator  in  foretelling  the  state  of  the  weather  ; 
and  according  to  their  form  they  are  divided  into  three  classes, 
called  cirrus,  cumulus,  and  stratus.  There  are  four  other  forms 
in  which  these  are  blended,  known  as  cirro-cumulus,  cirro- 
stratus,  cumulO'Stratus,  and  nimbus.  Though  it  is  easy  to 
distinguish  the  first  three  classes  when  their  forms  are  well 
characterized,  it  is  often  very  difficult  to  accurately  designate 
the  blended  forms,  as  some  observers  will  call  cirro-stratus 
what  others  would  designate  curnulo-stratus. 


CIRRUS. 


The  Cirrus  are  composed  of  thin  filaments,  resembling  a 
brush,  and  at  times  woolly  hair  or  slender  network.     These 


66 


SIMPLE    ELEMENTS    OF   NAVIGATION. 


are  the  most  elevated  clouds,  and  their  appearance  often  pre- 
cedes a  change  of  weather.  In  summer  they  announce  rain  ; 
in  winter,  frost  or  snow. 

The  Cumulus  appear  in  the  form  of  a  hemisphere  resting 
on  a  horizontal  base ;  sometimes  these  hemispheres  rest  one 


CUMULUS. 

upon  the  other,  and  form  those  great  clouds  which  accumu- 
late on  the  horizon,  and  look  like  distant  mountains  covered 
with  snow.     They  predict  warm  southerly  winds. 
The  Stratus  are  the  horizontal  bands,  which  form  fre- 


STRATUS. 

quently  at  sunset,  and,  combining  with  the  other  two  forms, 
indicate  what  might  be  expected  in  the  state  of  the  weather — 
moisture. 


CAUSES   THAT    AFFECT    NAVIGATION   AT    SEA.       67 

Cirro-cumulus  appear  as  a  number  of  little  round,  fleecy 
clouds,  and  foretell  beat. 


CIRRO-CUMULUS. 

Cirro-stratus  are  composed  of  little  bauds  of  filaments, 
more  compacted  than  those  of  the  cirrus,  and  not  so  high,  of 
a  grayish  tint,  and  hardly  ever  fail  to  form  rain. 


CIRRO-STRATUS. 


Ciimulo-stratus  are  formed  from  the  cumulus  clouds  be- 
coming more  dense,  or  heaped  together.  If  they  appear  in 
the  morning,  rainfall  may  occur,  but  will  cease  near  noon  as 
a  rule;  and  when  they  form  about  noon,  rain  may  follow,  but 
will  cease  towards  evening. 


68 


SIMPLE   ELEMENTS   OF   NAVIGATION. 


CUMULO-  STRATUS. 

Nimbus    are  the  dense   black  clouds  \vit-h   gray-fringed 
edges,  and  are  variously  composed  of  the  other  forms,  mainly 


NIMBUS. 

of  the  compacted  cumulus,  and  are  always  accompanied  by 
rain,  wind,  or  storms. 

Storms  and  Currents  are  most  uncertain  causes  that  en- 
danger the  position  of  the  ship  at  sea,  and  should,  be  carefully 
guarded  against. 

Storms.  Wind  is  air  in  motion  caused  by  difference  of 
temperature,  and  the  direction  is  designated  by  the  point  of 
the  compass  from  which  it  blows.  When  this  difference  of 
temperature  is  great  the  motion  of  the  wind  is  exceedingly 
heightened,  and  in  some  cases  in  the  region  of  a  mountainous 


CAUSES   THAT   AiTKCT    NAVIGATION    AT    SEA.       G'.> 

coast  it  rushes  suddenly  down  with  almost  irresistible  force. 
The  wind  blowing  in  great  violence  in  one  direction  is  called 
a  straight-line  gale.  The  most  severe  gales  met  with, 
however,  at  sea,  are  commonly  known  as  revolving'  storms, 
variously  called  hurricanes,  typhoons,  and  cyclones,  according 
to  the  locality  in  which  they  blow.  These  revolving  storms 
have  two  mofious — one  in  a  circle  like  a  whirlwind,  and  the 
other  a  forward  movement  on  a  curved  track.  Knowing 
these  two  movements,  the  problem  then  to  be  considered  in  re- 
lation to  the  safety  of  the  ship  is  .  1st.  Ascertain  the  charac- 
ter of  the  storm  and  locate  its  centre.  2d.  Determine 
which  half  of  the  storm -centre  the  ship  is  in.  3d.  The  di- 
rection in  which  the  storm  is  moving.  4th.  What  to  do  with 
the  ship  to  escape  the  centre,  or  take  advantage  of  the  fail- 
winds. 

The  character  of  the  storm  is  indicated  by  the  weight  of 
the  atmosphere,  and  as  heat  and  moisture  are  the  principal 
causes  of  the  variation  in  the  weight  of  the  atmosphere,  it 
follows  that  the  temperature  and  degree  of  moisture  should  be 
known  at  the  time  of  observation.  The  barometer  is  an  in- 
strument for  measuring  the  weight,  the  thermometer  gives 
the  temperature,  and  the  hygrometer  the  degree  of  moisture 
in  the  air. 

The  Barometer.  There  are  various  forms  of  the  barome- 
ter, but  the  one  best  suited  for  observations  is  the  mercurial, 
consisting  of  a  brass  tube  about  33  inches  in  length,  the  ex- 
tremity of  which  is  inserted  into  a  small  cistern.  In  order  to 
maintain  the  mercury  in  the  cistern  at  the  same  level,  the  cis- 
tern is  constructed  partly  of  leather.  By  means  of  a  screw  at 
the  bottom,  the  surface  of  the  mercury  in  the  cistern  may  be 
so  adjusted  as  to  have  it  always  at  the  place  from  which  the 
scale  commences.  The  upper  part  of  the  tube  is  cut  through 
so  as  to  exaose  the  column  of  mercury.  Attached  to  one  side 
of  this  opening  is  a  scale  graduated  in  inches  and  parts  ;  and 
inside  this  slides  a  small  tube  carrying  a  vernier,  which  is 
moved  up  or  down  by  a  small  thumb-screw.  A  thermometer 
is  attached  to  the  barometer  to  indicate  the  temperature  of 
the  mercury  in  the  cistern.  When  suspended  for  use  the 
barometer  should  hang  freely  in  a  vertical  position,  exposed 
in  the  shade  where  no  local  heat  or  cold  is  liable  to  affect  it. 


SIMPLE   ELEMENTS   OF 


[NORTHERN   HEMISPHERE] 


[SOUTHERN  HEMISPHERE] 


THE  Two  MOTIONS  OP  A  CYCLONE. 


CAUSES   THAT   AFFECT    NAVIGATION    AT    SKA.       71 


Whenever  opportunity  offers,  the  barometer  should  be  com- 
pared \vith  a  standard,  and  the  corrections  noted. 

A  want  of  absolute  information  as  to  the  mean  level  of  the 
mercury  will  not  prevent  advantage  being  taken  of  barometri- 
cal observations  in  practical  navigation  ;  yet  it  is  best  to 
know  the  mean  level  at  the  position  of  the  observer. 
Monthly  charts  issued  by  the  Hydrographic  Office  of  the 
Xavy  Department,  a  branch  office  of  which  is  located  at  all 
large  maritime  cities  in  the  United  States,  gives  the  mean 
level  of  the  barometer  at  a  great  many  positions  in  the  Atlan- 
tic and  a  few  in  the  Pacific  Ocean.  In  the  absence  of  these 
charts,  the  following  table,  according  to  ]\Iaury,  is  most  re- 
liable for  each  parallel  of  latitude  in  the  North  Atlantic,  from 
the  equator  to  seventy  degrees  North. 


North 

Height  of 

North 

Height  of 

North 

Height  of 

latitudes. 

barometer. 

latitudes. 

barometer. 

latitudes. 

barometer. 

Inches. 

o 

Inches. 

0 

Inches. 

Equator. 

29.918 

25 

30.119 

50 

30.001 

5° 

29.910 

30 

30.182 

55 

29.989 

10 

29.941 

35 

30.162 

60 

29.878 

15 

29.989 

40 

30.111 

65 

29.839 

20 

30.052 

45 

30.052 

70 

29.800 

The  Thermometer  is  an  instrument  founded  on  the  prin- 
ciple that  most  bodies  expand  by  heat  and  contract  by  cold. 
Its  construction  differs  from  the  barometer  in  having  the  tube 
closed  at  both  ends.  There  are  three  descriptions  of  ther- 
mometers in  common  use,  constructed  on  the  same  principle, 
but  differing  in  the  division  of  their  respective  scales. 
Fahrenheit's  thermometer  is  the  one  generally  used  in 
America,  and  is  marked  from  melting  ice  at  82  degrees  to  boil- 
ing water  at  212  degrees,  the  interval  being  divided  into  180 
equal  parts.  The  same  graduation  is  extended  downwards  to 
zero  and  below.  The  bulb  should  be  kept  dry,  and  exposed 
in  the  shade  to  the  open  air. 

The  Hygrometer  is  simply  a  thermometer  with  the  bulb 
wrapped  in  a  little  muslin  bag,  or  a  kind  of  wick  reaching 
from  it  into  a  small  cistern  of  water  from  one  to  three  inches 
awray.  The  difference  in  the  reading  of  the  wet  and  dry 
thermometers  gives  the  evaporating  power  of  the  air,  upon 


72  SIMPLE   ELEMENTS   OF   NAVIGATION. 

which  depends  the  amount  of  moisture  present.  The  ther- 
mometer and  hygrometer  should  be  enclosed  in  a  case  having 
a  lattice  front. 

Approach  of  A  Storm.  The  indications  of  the  approach 
of  a  storm  are  :  a  restless  state  of  the  barometer  ;  a  hard  gray 
sky  or  one  having  a  greenish  tint  ;  a  blood-red  or  bright-yellow 
sunset;  a  heavy  swell,  and  a  thick,  lurid  appearance  of  the  sky, 
in  connection  with  a  general  threatening  condition  of  the 
weather.  No  great  storm  ever  sets  in  with  a  steady  rising 
barometer,  and  it  will  blow  a  storm  whenever  the  barometer 
rises  or  falls  suddenly.  The  barometer  will  not  rise  much 
in  front  of  a  slowly  moving  storm,  but  the  banking  up  of  air 
on  the  border  in  front  of  a  rapidly  moving  storm  will  often 
cause  it  to  rise  suddenly.  A  very  rapid  fall  of  the  barometer 
after  fairly  entering  the  storm  may  be  regarded  as  evidence 
of  a  very  violent  storm  of  small  diameter,  while  a  gradual  fall 
would  indicate  the  contrary.  In  the  North  Atlantic,  any- 
where between  the  equator  and  30  degrees  north  latitude, 
when  the  barometer  is  observed  to  fall  at  the  rate  of  .02  of  an 
inch  per  hour  and  to  reach  a  point  from  .2  to  .3  below  the 
mean  level,  precautions  should  betaken  against  the  approach- 
ing storm.  Gales  will  last  a  longer  or  shorter  time,  and  are  fore- 
told twelve  hours  at  least  and  sometimes  twenty-four  hours  in 
advance,  according  as  the  rise  or  fall  of  the  barometer  is  more 
or  less  rapid.  A  northerly  wind  will  produce  a  high  or  rising 
barometer,  and  a  southerly  wind  a  low  or  falling  barometer  ; 
hence,  the  barometer  being  very  high,  with  northerly  winds,  a 
sudden  fall  accompanied  by  rise  of  the  thermometer  indicates 
that  the  wind  will  back  with  great  force  to  the  southward. 
Should  the  barometer  be  very  low,  a  sudden  rise  with  a  fall- 
ing thermometer  predicts  a  change  of  wind  from  the  SW.  to 
the  NW.  and  a  northerly  gale.  In  winter  a  sudden  fall  of 
the  barometer  and  the  thermometer  towards  the  freezing- 
point  indicates  snow.  Off  the  coast  of  the  United  States  the 
region  traversed  by  the  Gulf  Stream  is  remarkable  for  its 
high  temperature  and  for  squally  and  uncertain  weather, 
especially  in  winter.  When  the  winds  from  W.  to  SW.  blow 
a  gale  the  heat  of  the  atmosphere  reaches  its  extreme,  while 
beyond  the  northern  and  eastern  limits  of  the  storm  is  ex- 
tremely cold.  Should  a  storm  be  blowing  fiom  the  NE 


CAUSES   THAT    AFFECT   NAVIGATION"    AT    SKA.      73 

and  the  barometer  begin  to  fall  with  a  rise  of  the  thermome- 
ter, the  wind  will  haul  to  the  K.  ami  SK.;  but  should  the 
barometer  suddenly  rise  more,  with  a  falling  thermometer,  the 
wind  is  liable  to  shift  suddenly  and  with  great  foree  to  the 
NW.,  and  come  out  clear  and  cold. 

To  Locale  the  Centre.  When  facing  the  wind  the  centre 
of  the  storm  will  bear  eight  points  to  the  right  in  the 
northern  or  eight  points  to  the  left  in  the  southern  latitudes; 
because  in  the  northern  portion  of  the  globe  the  wind  within 
the  storm  revolves  from  the  right  to  left  or  left-handed,  and  in 
the  southern  part  the  wind  revolves  from  the  left  to  right  or 
right-handed.  Hence,  when  north  of  the  equator,  at  the  west 
point  of  the  storm-circle  the  wind  is  north  and  the  centre  bears 
east  ;  and  south  of  the  equator,  at  the  west  point  of  the  storm- 
centre  the  wind  is  south  and  the  centre  bears  east.  If  the 
barometer  falls  at  the  rate  of  .03  of  an  inch  per  hour  and  gets 
from  .4  to  .5  below  the  mean  level,  the  indication  is  that  the 
centre  of  the  storm  is  about  two  hundred  miles  off  ;  with  an 
hourly  fall  of  .05  to  a  point  .78  of  an  inch  below  the  mean 
level,  the  vessel  may  be  considered  about  one  hundred  miles 
off.  With  a  fall  of  .09  to  1.5  per  hour  below  the  mean  level, 
the  vessel  will  be  very  close  to  the  centre,  if  not  in  it.  When 
the  barometer  begins  to  rise  again,  at  first  very  quickly  and 
afterward  with  a  more  moderate  movement,  the  centre  of  the 
storm  will  be  travelling  away  from  the  ship,  and  the  danger  is 
over. 

Semicircles  of  the  Storm.  The  storm-circle  is  divided 
into  two  equal  parts  by  the  storm  track,  and  that  portion  on 
the  right  side  looking  in  the  direction  of  the  track  is  termed 
the  right  semicircle,  while  that  portion  to  the  left  is  called 
the  left  semicircle. 

In  the  right  semicircle  the  change  of  wind  will  be  to  the 
right,  and  in  the  left  semicircle  the  change  will  be  to  tie 
left ,  therefore  the  first  change  of  wind  will  indicate  which 
half  of  the  storm-circle  the  ship  is  in.  Should  the  vessel  be 
directly  on  the  track  of  the  storm  or  near  it  on  either  side 
there  would  be  no  perceptible  change  of  wind,  but  a  falling 
barometer  would  indicate  the  vessel  was  in  front  and  a  rising 
barometer  in  rear  of  the  storm. 

Direction  of  Storm  Track.  The  approximate  direction 
in  which  the  storm  is  moving  may  be  found  by  plotting  on 


74  SIMPLE    ELEMENTS   OF   NAVIGATION. 

the  chart  the  position  of  the  ship  and  centre  of  the  storm  on 
two  or  more  bearings  as  the  wind  changes,  using  the  distance 
of  the  centre  by  barometer,  and  keeping  an  accurate  account 
of  the  distance  made  by  the  ship  in  the  interval. 

To  Avoid  the  Centre.  Having  ascertained  the  above 
data,  it  becomes  necessary  now  to  determine  what  to  do  with 
the  ship  to  escape  the  centre  or  place  the  vessel  in  a  position 
to  incur  the  minimum  amount  of  danger  or  take  advantage  of 
the  fair  winds  as  the  case  may  be. 

The  rules  to  be  observed  are  given  in  the  following  storm- 
cards. 


EAST  WIND  CH.TO  SD.H.STR.TACK  ' 

— : 


•CH.TO  ND.RUN    WNW. 

PR  H.P.TACK 


STORM    CARD 
NORTHERN    HEMISPHERE 


ABBREVIATIONS 
CH.: 


The  courses  here  given  are  for  the  wind  2  points 
on  the  starboard  quarter,  but  if  sea  and  wind 
permit   bring   the   wind  broad  on  the  quarter. 
If  in  either  of  these  positions  there  be  danger 
of  broaching-to,  run  before  the  wind  until 
more  moderate,  and  then  bring  wind  on 
starboard  quarter.   A  ship  hove-to  hav- 
ing the  wind  steady  is  on  the  storm- 
track.      Run   before  the   wind ; 
note   the   course   and 
keep    it. 


CH.TO  SD.RUN  ESt. 

OR  H.P.TACK 


Currents.  A  current  is  a  progressive  motion  of  the  water, 
occasioned  by  prevailing  winds  and  differences  of  temperature 
and  density,  and  causes  all  floating  bodies  to  move  in  the  di- 
rection of  its  set.  The  set  is  that  point  of  the  compass  towards 


CAl  SKS    THAT    AI'FK<T    NAVIGATION    AT    SKA.      7  ,"> 

which  the  waters  run,  and  its  drift  is  the  rate  it  runs  per  hour. 
The  effect  of  a  constant  or  prevalent  wind  produces  what  is 
called  a  drift  cm-rent,  is  generally  shallow,  ancj  hardly  ever 
exceeds  half  a  mile  per  hour  with  a  good  breeze.  The  accu- 
mulation of  the  drift  into  a  collective  mass  by  the  intervention 
of  some  obstacle  produces  what  is  called  a  stream  current. 
It  takes  the  direction  imposed  by  the  obstacle,  and  in  many 
cases  is  a  deep,  powerful  stream,  not  unlike  a  river  in  the  ocean. 
These  two  forms  of  current  cause  a  constant  circulation  to  be 
going  on  in  the  waters  of  the  globe,  and  are  usually  marked  on 


WEST  WIND  CH.TOSD 


CH.TC  NO.RL 

OR  H.STR.J 


STORM 
SOUTHERN    HEMISPHERE 


ABBREVIATIONS 


D.=  NORTH  WARD 
ED.         EASTWARD. 

.=  SOUTHWARD. 
WD.  =  WESTWARD. 


STARBOARD 


REMARKS. 

The  courses  here  given  are  for  the  wind  2  points 

on  port  quarter,  but  if  sea  and  wind  permit  bring 

the  wind  broad  on  the  quarter.     If  in  either  of 

these  positions  there  be  danger  of  broaching- 

to,  run  before  the  wind  until  more  moderate, 

and   then    bring   the   wind    on   the  port 

quarter.      A  ship  hove-to  having  the 

wind  steady  is  on  the  storm-track. 

Run  before  the  wind  ;  note  the 

course  and  keep  it. 


EAST  WIND  CH.TO  NO.H.P,;T»CK. 

CH.TO.SD.RUN  WSW. 
OR  H.STR.TACK. 


the  charts  with  the  set  and  drift  given.  As  they  are  liable  to 
vary  in  both  speed  and  direction  and  temporary  eddies  not 
marked  on  the  chart,  their  existence  and  influence  may  be 
found  by  a  comparison  between  the  position  by  dead-reckon- 


76  SIMPLE   ELEMENTS   OF   NAVIGATION. 

ing  and  that  by  observation,  corroborated  by  a  change  in  the 
temperature  or  density  of  the  water. 

Current  Sailing".  With  the  set  and  drift  of  a  current  known, 
it  can  be  allowed  for  in  the  following  manner  :  Draw  a  line 

AB  on  the  chart  in  the  direction  of 
the  set,  and  from  the  position  of  the 
ship  A  lay  off  on  this  line  AB  equal 
to  the  hourly  drift,  taking  the  meas- 
urement from  any  convenient  scale, 
say  an  inch  to  the  mile.  With  the 

A  same  scale  at  A  erect  a  perpendicular 

to  AB,  and  lay  off  on  this  perpendic- 
ular AC  equal  to  the  vessel's  speed  per  hour  ;  draw  CD  paral- 
lel to  AB,  and  BD  parallel  to  AC.  In  order  then  to  make 
good  the  intended  course  AD,  and  keep  the  objective  point  P 
constantly  on  the  same  line  of  bearing,  the  vessel  will  have  to 
steer  in  the  direction  of  A C.  The  scale  on  the  chart  will  be 
found  too  small  to  give  a  working  size  to  the  figure  ;  however, 
it  can  be  used  by  multiplying  the  drift  of  the  current  and  the 
rate  of  the  vessel  by  some  convenient  number. 

Iceberg's.  The  currents  from  the  polar  regions  bring  with 
them  great  quantities  of  floating  ice,  and  the  presence  of  these 
icebergs  constitutes  a  very  serious  danger  to  navigation.  The 
latitudes  in  which  these  floating  islands  are  to  be  met  with  are 
generally  marked  on  the  chart,  and  when  in  those  regions  no 
precaution  should  be  neglected  to  discover  them  before  the 
danger  becomes  too  great. 

A  large  iceberg  will  denote  its  presence,  even  on  the  darkest 
night,  by  a  sort  of  whiteness  or  halo  known  as  "ice  blink." 
The  echo  of  a  gun  or  steam-whistle  is  liable  to  detect  the 
presence  of  an  iceberg ;  and  should  one  be  to  windward,  the 
temperature  of  the  air  would  indicate  its  proximity.  The 
temperature  of  the  water  cannot  be  relied  upon  as  a  means  of 
detecting  the  presence  of  ice. 

Should  a  berg  be  discovered,  always  endeavor  to  pass  on  the 
weather  side  on  account  of  the  loose  pieces  drifting  more 
rapidly. 


AIDS   TO   NAVIGATION.  77 


CHAPTER  X. 

AIDS  TO  NAVIGATION. 

WHEN  the  vesse1  on  lier  course  leaves  the  deep  water  and 
comes  upon  soundings,  the  fact  is  at  oiice  known  by  a  change 
in  the  temperature  of  the  water  and  the  blue  appearance  of 
the  sea  changing  to  a  decided  green  color.  The  evidence  of 
approaching  shore  is  seen  in  the  presence  of  birds,  floating 
objects,  nature  of  the  swell  of  the  sea,  and  the  sense  of  smell. 
The  land  is  rirst  seen  in  an  outline  resembling  a  thick  cloud, 
but  which  can  hardly  be  mistaken. 

In  making  the  proper  point  or  working  the  way  into  port 
assistance  is  afforded  in  the  nature  of  the  shore,  complexion  of 
the  land,  and  configuration  of  the  coast-lines,  as  well  as  any 
isolated  tree,  church  spire,  windmill  or  prominent  mountain. 

In  addition  to  these,  all  maritime  countries  have  established 
a  well-concerted  series  of  landmarks  as  aids  to  navigation, 
such  as  light-houses,  light-vessels,  buoys,  beacons,  and  fog- 
signals. 

Light-houses.  The  light-house  is  not  only  a  house  or  tower 
especially  adapted  for  showing  a  light  at  night,  but  serves  as 
a  landmark  by  day.  They  are  sufficiently  diversified  by 
different  characteristics  to  properly  define  their  respective 
positions. 

As  we  approach  the  shore  from  seaward  the  most  salient 
points  of  the  coast-line  are  marked  by  first-class  light-houses 
having  the  greatest  power  and  range.  They  are  planted  so 
close  to  each  other  as  to  prevent  the  vessel  from  getting  within 
any  outlying  danger,  except  in  a  dense  fog,  without  catching 
sight  of  one  or  more  of  them.  They  give  warning  of  the 
position  of  the  vessel,  and  enable  au}r  errors  to  be  corrected 
before  the  ship  shall  have  approached  too  near  the  coast  for 
safety. 

The  secondary  capes,  reefs,  and  sand-banks,  to  which  it  is 
prudent  to  give  a  good  offing,  are  marked  by  second-  and  third 
class  light  houses,  and  the  range  is  regulated  by  the  distance 
at  which  it  is  necessary  to  see  them.     During  thick  weather 


78 


SIMPLE    ELEMENTS    OF    NAVIGATION. 


AIDS   TO    NAVIGATION.  79 

the  range  of  the  first-class  lights  is  greatly  diminished  in 
power  and  extent  when  those  of  the  second  class  assist  to  fill 
up  the  vacancy  thus  caused  in  the  primary  illumination. 
Lights  of  these  classes  are  also  placed  to  mark  the  mouths  of 
rivers  and  the  entrance  to  ports  only  accessible  by  narrow 
channels,  and  to  point  out  the  exact  course  which  should  be 
steered. 

Near  the  port  or  anchorage  a  small  harbor  light  is  placed 
upon  one  or  each  of  the  banks,  piers,  or  breakwater  as  a  guide 
to  a  good  berth.  Many  of  these  small  lights  belonging  to 
tidal  harbors  are  not  exhibited  until  the  tide  has  reached  a 
certain  determined  height. 

Order  of  Lights.  In  the  United  States  the  lights  are 
divided  into  six  orders.  Lights  of  the  first  order  are  those 
established  to  give  warning  of  the  approach  to  land  ;  those  of 
the  second,  to  mark  the  secondary  points  or  headlands  along 
the  sea  coast  and  the  approach  to  bays  and  sounds  ;  third-order, 
lights  are  used  in  bays  that  are  of  considerable  width  and 
intricacy,  and  for  the  coast  of  lakes  ;  lights  of  the  fourth,  fifth, 
and  sixth  orders  mark  the  most  prominent  points,  headlands, 
or  shoals  in  the  long  bays,  sounds,  or  obstructions  in  rivers, 
and  piers  or  wharves. 

Character  of  Lights.  In  addition  to  the  division  of  lights 
according  to  their  position  for  illumination,  provision  is  made 
for  their  easy  distinction  so  as  to  not  mislead  by  a  close  resem- 
blance of  one  to  the  other.  To  this  end  lights  are  divided 
into  several  distinctive  characters — the  fixed,  revolving,  flash 
or  intermittent,  and  double  light  on  one  or  two  towers. 

The  Fixed  Light  is  one  which  exhibits  a  regular  and  steady 
appearance,  and  is  not  subject  to  any  change. 

The  Revolving  Light  gradually  increases  to  a  maximum 
and  diminishes  to  a  minimum  until  wholly  extinguished  at 
equal  intervals  of  half  a  minute,  one,  two,  or  three  minutes,  and 
sometimes  thrice  a  minute.  It  is  produced  by  the  revolution 
of  a  three-  or  four-sided  frame  having  large  reflectors  grouped 
on  each  side,  with  their  axes  parallel. 

The  revolving  light  is  subdivided  into  other  classes,  such  as 
revolving  white,  revolving  red  and  white,  revolving  red  with 
two  whites,  or  revolving  white  with  two  reds,  obtained  by  the 
revolution  of  a  frame  whose  sides  present  red  and  white  lights 
in  succession. 


80  SIMPLE   ELEMENTS   OF   NAVIGATION. 


LIGHT-HOUSE  ON  ALLIGATOR  REEF,  FLORIDA  REEFS. 


AIDS   TO    NAVIGATION. 


81 


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SIMPLE    ELEMENTS   OE   NAVIGATION. 


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13 

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AIDS   TO    NAVIGATION.  83 

The  Flash  or  Intermittent  Light  is  one  in  which  the  ray 
suddenly  appears,  remains  visible  for  a  moment,  and  afterwards 
is  again  suddenly  eclipsed  for  a  brief  interval.  This  is  due  to 
the  perpendicular  motion  of  circular  shades  in  front  of  the 
reflector  by  which  the  light  is  alternately  revealed  and  hidden. 
This  light  and  the  revolving  light  are  sometimes  combined  to 
form  the  revolving  flash  light. 

The  Double  Lights  are  seldom  used  except  where  a  leading 
line  is  needed  as  a  guide  for  taking  some  narrow  channel  or 
avoiding  some  danger.  They  are  generally  exhibited  from 
two  towers,  one  of  which  is  higher  than  the  other,  and  pro-' 
duce  marked  characteristic  distinction  or  serve  as  a  range  to 
avoid  danger.  In  the  first  case  the  distance  between  the  lights 
is  such  as  to  prevent  the  two  being  blended  into  or  supposed 
to  be  one  lightt  within  the  limits  of  their  ranges.  In  the 
second  case  they  are  so  arranged  they  will  be  seen  to  separate 
the  moment  of  departure  from  the  straight  range  line  they  are 
placed  to  mark.  Frequently  a  very  small  arc  is  illuminated 
by  one  light  which  can  be  seen  before  encountering  danger. 

Colored  Lights.  Another  means  of  distinguishing  the 
various  lights  is  in  their  color :  some  are  red,  with  an  intense 
ruddy-like  splendor  ;  others  white,  and  some  blue  or  green. 
However,  colored  lights  should  be  observed  with  caution,  as  the 
use  of  coloring  matter  reduces  in  great  proportions  the  in- 
tensity of  the  light ;  and  the  atmospheric  conditions  sometimes 
determine  the  color,  which  may  lead  to  mistake  as  to  the  real 
color  of  the  light.  It  has  been  observed  that  during  foggy 
weather  white  lights  become  of  a  reddish  color  or  tinge  ;  green 
appears  to  approach  in  color  or  become  white  ;  and  blue  lights 
are  not  visible  or  change  to  so  pale  a  violet  tint  as  to  be  mis- 
taken for  white.  But  if  there  be  two  lights  of  different  color, 
such  as  red  and  white,  one  becomes  intensely  red  and  the  other 
a  red  tinge,  both  preserving  their  distinctive  character.  If 
green  were  in  place  of  red,  the  two  lights  would  appear  to  be 
red  and  white  without  a  marked  difference  in  color.  Some 
heavy  fogs,  however,  allow  all  the  luminous  rays  to  pass 
through  them  equally  without  coloring  them,  and  only  have 
the  effect  of  diminishing  their  intensity.  With  equal  intensity, 
the  red  light  will  be  seen  farther  than  the  white  light ;  but  if 
the  two  are  used,  the  white  light  will  cease  to  be  visible  before 
the  red  light. 


84 


SIMPLE    ELEMENTS    OF    NAVIGATION. 


The  electric  light  possesses  a  great  distinction  of  color,  but 
very  little  superiority  in  penetrating  power  in  thick  weather, 
and  at  any  time  is  blinding,  or  its  distance  hard  to  ascertain. 

Range  of  Lights.  The  distance  at  which  a  light  may  be 
seen  depends  upon  its  intensity  and  height  above  the  sea  or  its 
luminous  and  geographical  range.  The  luminous  range  de- 


CRAIGHILL'S  GHA.NXEL  RA.NGE  LIGHTS. — HIGH  LIGHT. 

pends  upon  the  state  of  the  atmosphere  and  the  acuteness  of 
the  eye  of  the  observer. 

The  geographical  range  depends  upon  the  height  above  the 
level  of  the  sea,  upon  the  curvature  of  that  part  of  the  earth's 
surface  at  which  it  is  placed,  and  upon  the  value  of  atmos- 
pheric refraction. 


AIDS   TO   NAVIGATION. 


85 


In  the  United  States  the  heights  of  all  light-houses  are  given 
in  the  lists  and  nautical  books  for  mean  low-water,  together 
with  range  corresponding  to  different  heights  above  the  level 
of  the  sea  both  for  the  focal  point  and  the  eye  of  the  observer. 
In  some  countries  the  tables  are  made  out  with,  reference  to 
the  level  of  the  highest  water. 


J 


CRAIGHILL'S  CHANNEL  RANGE  LIGHTS. — Low  LIGHT. 

By  a  reference  to  the  chart,  light  list,  and  sailing  directions 
a  minute  description  and  sketch  of  all  light-houses  will  be 
found,  their  position  accurately  noted,  the  character  and 
brilliancy  of  the  light,  the  order  or  class,  bearings  on  which 
the  light  is  visible  or  obscured,  height  of  the  centre  of  the 
lantern  above  the  high- water  level  or  mean  low  tide  ;  height 


86 


SIMPLE    ELEMENTS   OF   NAVIGATION. 


also  of  the  building  from  the  base  to  the  vane,  and  its  form, 
color,  and  other  peculiarities. 

Light-ships.  The  seas  adjacent  to  the  coast  are  some- 
times interspersed  with  extensive  shoals  and  shifting  sand- 
banks, upon  which  it  is  impossible  to  erect  light-houses.  Nor 
can  those  already  built  upon  the  mainland  be  made  service- 
able in  directing  vessels  their  way  through  the  narrow  chan- 
nels running  in  all  directions,  distant  perhaps  fifteen  or 
twenty  miles  off  the  coast. 

In  approaching  the  sea  immediately  surrounding  these 
dangers,  light-ships  or  floating  lights  are  used  to  indicate  the 
exact  points  to  be  avoided.  They  also  serve  as  beacons 
against  variable  currents  and  reefs  which  are  hidden  at  cer- 
tain hours  by  the  high  tide. 

Each  light-ship,  like  the  light-house  on  shore,  is  dis- 
tinguished by  its  own  peculiar  aspect,  various  characteristics, 
and  certain  differences  in  telling  not  only  one  from  another, 
but  also  from  any  neighboring  light-house. 

How  appear.  When  seen  at  some  distance  a  light-ship 
closely  resembles  during  the  day  an  ordinary  vessel,  but  upon 
approaching  near  a  great  difference  between  the  two  is  seen. 
The  short  stout  masts  are  without  sails,  and  surmounted  by 
large  balls,  cages,  or  other  marks. 


LIGHT-SHIP. 


AIDS  TO   tf  AVWATtOtf.  87 

In  Great  Britain  the  bulls  of  light-ships  are  painted  red 
and  black.  In  the  United  States  they  are  painted  such  color 
and  in  such  a  way  as  the  Light-house  Board  may  designate, 
with  the  name  of  the  station  painted  on  the  sides  and  the 
number  of  the  vessel  on  the  stern. 

At  night  these  vessels  are  provided  with  one  or  more  lights, 
and  are  distinguished  by  their  number  and  position  as  well 
as  characteristic  distinction — such  as  single  or  double  fixed 
lights,  revolving  lights  with  varying  intervals  of  darkness  be- 
tween the  beams,  or  with  colored  beams  alternating  with 
white,  or  colored  beams  only. 

When  two  lights  are  used,  it  is  usually  the  custom  to  place 
one  higher  than  the  other. 

Few  instances  are  on  record  of  a  light-ship  having  broken 
loose  from  her  moorings.  If,  however,  the  ship  should  be 
driven  from  its  place  by  the  force  of  the  elements,  so  that  its 
light  may  become  a  source  of  danger,  means  are  provided  for 
signalling  by  flags  or  the  firing  of  a  gun.  No  one  except 
those  belonging  to  the  light-ships  is  ever  permitted  to  live  on 
board  or  to  remain  at  night,  unless  necessarily  detained  by 
stress  of  weather,  or  wrecked  persons  who  may  be  compelled 
to  take  temporary  refuge  on  board. 

Buoys  are  the  next  very  important  marks  that  contribute 
greatly  as  aids  to  navigation.  They  are  exceedingly  numer- 
ous, and  are  invaluable  as  guiding  marks  by  day  through  nar- 
row channels  and  warning  marks  for  isolated  dangers.  They 
are  not  very  serviceable  at  night,  being  unilluminated  ;  how- 
ever, buoys  have  been  lit  in  many  instances  by  the  application 
of  compressed  gas  confined  within  the  buoy;  and  it  has  been 
proposed  to  connect  them  with  wires  all  around  the  coast,  and 
to  light  them  simultaneously  with  electricity. 

Distinction.     Their  chief  elements  of  distinction  are  the 
form,  size,  and  color,  which  may  be  supplemented  by  the  ad- 
dition of  a  shape— such   as  globe,  diamond,  triangle,  etc.— 
mounted  on  top  of  the  mast  fixed  in  the  head  of  the  buoy. 

Names  of  Buoys.  The  names  of  the  various  forms  are  so 
unsettled,  that  but  few  persons  can  accurately  state  what  con- 
stitutes the  characteristic  of  each.  However,  the  descriptive 
titles  of  buojrs  are:  the  nun,  can,  conical,  convex,  spiral, 
drum,  cylinder,  spherical,  spar,  mast,  and  cask.  These  terms 
are  found  to  vary  at  different  places,  and  are  employed  to  give 


SIMPLE   ELEMENTS   OP   NAVIGATION". 

exactly  opposite  indications  ;  also,  intimations  conveyed  by 
colors  vary  at  different  places :  hence,  reference  to  name  or 
disposition  of  colors  is  apt  to  lead  to  some  confusion. 

In  France  a  uniform  system  of  coloring  is  used,  and  on 
each  is  painted  either  the  entire  or  abridged  name  of  tbe  rock 
or  bank  that  it  marks  ;  those  belonging  to  the  same  channel 
are  numbered  serially,  commencing  to  seaward.  Those  to 
mark  the  starboard  side  are  painted  red,  having  a  white  crown 
a  little  below  the  summit,  and  bear  the  even  numbers.  Those 
to  mark  the  port  side  are  painted  black,  and  bear  odd  num- 
bers. Those  which  may  be  left  indifferently  on  either  side 
are  painted  with  horizontal  stripes  alternately  red  and  black, 
bear  names,  but  no  numbers.  The  red  and  black  are  varied,  as 
circumstances  require,  by  painting  in  white  designs  of  checks, 
vertical  bands,  etc. 

In  England  the  entrances  to  channels  or  turning-points  are 
marked  by  conical  buoys  with  or  without  staff,  and  globe  or 
triangle,  cage,  etc.  Single-colored  can-buoys,  either  red  or 
black,  mark  the  starboard  side,  and  buoys  of  the  same  shape 
and  color,  either  checkered  or  vertical-striped  with  white, 
mark  the  port  side.  Other  distinctions  are  used,  when  re- 
quired, by  the  employment  of  conical  buoys  with  or  without 
staff,  globe,  or  cage,  globes  being  on  the  starboard  side  and 
cages  on  the  port  hand.  Where  a  middle  ground  exists  in  a 
channel,  each  side  of  it  is  marked  by  a  buoy  of  the  color  in  use 
in  that  channel,  but  with  annular  bauds  of  white,  and  with  or 
without  staff,  diamond,  or  triangle.  In  case  of  its  being  of 
such  extent  as  to  require  intermediate  buoys,  they  are  colored 
as  if  on  the  side  of  a  channel.  At  times  the  outer  buoy  is 
marked  by  a  staff  and  diamond,  and  the  inner  end  by  a  staff 
and  triangle.  Wrecks  are  marked  by  green  nun-buoys  placed 
on  the  wreck  next  to  mid-channel,  with  "  Wreck"  painted 
thereon;  also  two  balls  or  two  lights,  as  the  case  maybe. 

Each  buoy  is  marked  with  a  running  number,  and  the  name 
of  the  locality  where  it  belongs. 

In  the  Netherlands,  with  few  exceptions,  white  buoys  must 
be  left  on  the  starboard  hand  on  entering  the  channel  from 
seaward,  and  black  buoys  on  the  port  hand.  Outside  buoys, 
and  those  indicating  where  the  division  of  a  channel  begins, 
are  painted  red.  In  Belgium  the  same  system  prevails.  In 
Norway  and  Sweden  a  white  stake  with  a  broom  turned  up- 


AIDS   TO   NAVIGATION.  89 

wards  denotes  that  Hie  shoal  lies  to  the  north  or  east  of  the 
mark.  A  black  stake  with  a  broom  turned  downwards  de- 
notes that  the  danger  lies  to  tuc  south  or  west  of  the  mark. 
A  stake  with  white  and  black  horizontal  stripes,  surmounted 
by  a  ball  or  a  pole  with  a  cross  at  the  top,  may  be  passed  on 
either  side. 

In  Russia  the  system  is  nearly  the  same  as  in  Norway,  with 
this  addition  for  the  open  sea  :  a  red  broom  open  upwards  on 
a  red  pole  means  that  the  danger  lies  to  the  north  ;  a  black 
broom  open  downwards  on  awhile  pole  means  that  the  danger 
lies  to  the  south.  Two  black  brooms  on  a  black  and  white 
checkered  pole  mean  that  the  danger  lies  to  the  west  ;  and 
a  black  pole  with  cross  at  the  top  surmounted  by  a  ball  means 
that  a  vessel  can  pass  on  all  sides. 

In  the  United  States  the  largest  descriptions  of  buoys  are 
used  to  mark  approaches  to  channels,  seaward  bars,  and  iso- 
lated shoals  or  other  obstructions  to  navigation  which  lie  at 
considerable  distance  from  the  coast.  First  and  second  class 
buoys  mark  the  approaches  to,  the  obstructions  in,  and  to  point 
out  and  mark  the  limits  of  channels  leading  to  the  principal 
ports  or  harbors  along  the  coast. 

They  also  mark  the  channels  and  obstructions  adjacent  to 
the  coast  and  those  in  the  large  bays  and  sounds.  Second 
and  third  class  buoys  mark  the  approaches  to,  and  channels 
and  obstructions  of,  the  lesser  harbors  and  bays.  Nun  and 
can  buoys  liable  to  danger  or  to  be  swept  away  by  floating  ice 
are  removed  on  the  approach  of  freezing  weather,  and  spar- 
buoys  put  in  their"  places.  Small  spar-buoys  mark  channels 
and  obstructions  in  shoal-water  navigation. 

Special  buoys,  such  as  spherical  and  cask  buoys,  colored  and 
numbered,  are  used  to  mark  special  localities.  All  buoj^s  are 
placed  in  the  best  position  to  mark  obstructions  or  define 
channels,  and  float  as  high  and  as  nearly  upright  as  possible 
during  the  strongest  wind  and  tide.  White  serial  numbers,  as 
large  as  the  class  of  buoy  will  permit,  are  placed  on  four 
sides  of  red  and  black  buoys,  and  other  distinguishing  marks 
are  made  to  show  as  prominently  and  at  as  great  a  distance  as 
possible. 

Different  channels  in  the  same  bay,  sound,  river,  or  harbor 
are  marked  as  far  as  practicable  by  different  descriptions  of 
buoys. 


90 


SIMPLE   ELEMENTS   OF   NAVIGATION. 


AIDS   TO   NAVIGATION.  91 

The  main  channel  is  marked  by  mm-buoys  ;  can-buoys  indi- 
cate secondary  channels,  and  spar-buoys  minor  channels. 
When  there  is  but  one  channel,  nun-buoys  properly  colored 
and  numbered  are  placed  on  the  starboard  side  and  can-buoys 
on  the  port  side. 

On  entering  the  channel  from  seaward  red  buoys  with  even 
numbers  are  placed  on  the  starboard  side  of  the  channel,  and 
must  be  left  on  the  starboard  hand  in  passing  in.  Black 
buoys  with  odd  numbers  are  placed  on  the  port  side  of  the 
channel,  and  must  be  left  on  the  port  hand  in  passing  in. 
Buoys  painted  with  red  and  black  horizontal  stripes  without 
numbers  are  placed  on  rocks  or  other  obstructions  with  chan- 
nels on  either  side  of  them,  and  maybe  left  on  either  hand  in 
passing  in.  Buoys  painted  with  black  and  white  vertical 
stripes  without  numbers  are  placed  in  mid-channel,  and  must 
be  passed  close  to  avoid  danger.  Buoys  to  mark  abrupt  turn- 
ing-points in  channels  or  obstructions  requiring  a  specific  and 
permanent  mark  are  fitted  with  staves  surmounted  by  balls, 
cages,  triangles,  or  other  distinctive  marks,  the  color  indicat- 
ing wThich  side  they  shall  be  passed.  Yellow  buoys  without 
numbers  are  used  to  mark  any  danger  at  a  quarantine  station. 

The  bearings  from  one  mid-channel  buoy  to  another  in  the 
order  of  passing  to  other  buoys  or  objects,  the  name  of  the 
station  or  position  occupied,  the  color,  number,  description, 
class,  depth  of  water  at  mean  low  tide,  kind  of  bottom,  and 
such  other  marks  to  aid  navigation  will  be  found  in  the  proper 
column  of  the  buoy  list. 

Beacons  are  small  but  durable  structures  of  timber,  mason- 
ry, or  iron,  placed  on  low,  outstretching  points  of  land,  rocks 
and  sand-banks,  shoals  or  elsewhere,  which  at  certain  times  of 
the  tide  are  hidden  from  view,  in  estuaries  and  broad  parts  of 
rivers.  They  serve  as  leading  marks  through  certain  chan- 
nels for  the  avoidance  of  special  dangers,  and  as  a  guide  for 
entering  harbors  or  anchorage  ground. 

Every  beacon  set  up  has  some  especial  characteristic,  so  that 
it  may  be  recognized,  being  usually  surmounted  with  a  char- 
acteristic head  in  the  form  of  a  globe,  diamond,  cross,  or  tri- 
angle. Beacons  are  painted  in  such  a  manner  that  the  color 
will  cause  them  to  be  well  denned  upon  the  background,  and 
those  on  sides  of  channels  are  painted  the  same  as  buoys. 
Some  of  these  beacons  are  provided  with  a  ladder  leading  up 


SIMPLE   ELEMENTS   OF   NAVIGATION. 


c 

OJ 


H 

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K 


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12; 

o 


PQ 


AIDS   TO    NAVIGATION.  93 

to  a  refuge  cage  above  the  high-water  mark,  capable  of  hold 
ing  several  persons.    As  a  general  rule,  beacons  are  not  lighted 
up  at  night;  yet  several  arrangements  have  been  devised  for 
lighting  beacons  on  detached  rocks  which  are  inaccessible 
during  rough  weather. 

Sound-signals.  The  various  marks  so  far  dealt  with  are 
those  which  depend  upon  the  sense  of  sight  only  ,  but  when 
sight  is  unavailing,  the  sense  of  hearing  naturally  suggests  it- 
self when  sound-signals  have  to  be  used  as  aids  to  navigation, 
especially  during  fogs,  mists,  and  snow-storms.  These  sound- 
signals  are,  with  certain  modifications :  sirens,  trumpets, 
steam-whistles,  bell-buoys,  whistling-buoys,  bells  struck  by 
machinery,  cannons,  rockets,  and  gongs. 

Gong's  are  sometimes  used  on  light-ships  and  for  close 
quarters,  having  an  effective  range  of  about  500  yards.  They 
are  of  most  use  in  harbors,  short  channels,  and  like  places, 
where  a  long  range  would  be  unnecessary. 

Rockets  are  used  in  light-houses  as  a  signal  where  it 
would  be  impossible  to  mount  large  pieces  of  apparatus.  It 
frequently  happens  that  the  sound-signal  intended  to  be 
heard  at  a  certain  distance  is  obstructed  or  deflected  by  inter- 
vening" obstacles;  the  rocket  in  this  case  overcomes  the  diffi- 
culty. The  charge,  usually  of  gun-cotton,  is  fitted  to  the  head, 
and  the  whole  projected  to  the  height  of  perhaps  1000  feet, 
when  the  charge  is  exploded,  and  sound  scattered  in  all 
directions,  with  greater  effect  than  the  report  of  a  gun. 
Some  of  these  rockets  have  been  heard  at  a  distance  of  twenty- 
five  miles. 

Cannon  are  used  for  various  purposes  in  connection  wiili 
signalling.  The  minute-gun  at  sea  indicates  that  the  vessel  is 
in  distress,  and  that  assistance  is  required.  On  some  light- 
ships the  cannon  is  used  to  attract  attention  of  shipwrecked 
life-boats.  They  are  also  used  as  warning  signals  on  head- 
lands and  dangerous  points  on  a  coast,  as  aids  to  navigation 
in  foggy  weather,  as  well  as  for  signalling  in  accordance  with 
an  arranged  code.  Owing  to  the  short  duration  of  sound,  the 
use  of  the  cannon  is  not  so  great  as  it  once  was,  as  the 
observer,  either  through  lack  of  attention  or  otherwise,  may 
not  hear  unless  prepared  for  it,  the  sound  being  liable  to  be 
quenched  by  local  sounds,  or  even  obliterated  by  a  puff  of 
wind.  The  interval  between  each  shot  was  formerly  fifteen 


94 


SIMPLE    ELEMENTS    OF   NAVIGATION. 


minutes,  but  recently  it  has  been  altered  to  ten  ;  owing,  how- 
ever, to  the  severe  labor  and  risks  accompanying  it,  this  inter- 
val is  of  considerable  irregularity. 

Bells  are  in  use  at  every  light-station,  and  at  many  they 
are  run  by  machinery  actuated  by  clockwork.  These  bells 
weigh  from  300  to  3000  pounds.  The  sound  of  a  bell  is 
curiously  fluctuating,  and  the  vibrations  of  the  largest  bells 
are  not  of  sufficient  intensity  to  yield  a  sound  capable  of  over- 
coming opposing  influences,  even  of  a  slight  nature,  and  the 
effective  range  is  at  times  very  doubtful.  However,  it  has 
been  shown  by  experiments  that  the  range  of  bell  sounds  can 
be  increased  with  the  rapidity  of  the  stroke  ;  it  has  also  been 
somewhat  increased  by  the  use  of  iron  reflectors.  By  this  it 
will  be  seen  that  the  bell  is  only  used,  like  the  gong,  for  short 
distances,  and  is  not  efficient  for  fog-signals  on  the  sea-coast. 
Owing  to  rough  weather,  the  noises  ol  the  surf  will  drown 
the  sound  to  seaward  altogether. 


OOURTENAY'S  WHISTLING-BUOY. 


AIDS   TO   NAVIGATION. 


05 


The  Whistling-buoy,  devised  by  Mr.  Courtenuy,  is  exten- 
sively employed  in  various  parts  of  the  world.  It  has  a  pow- 
erful whistle  fixed  at  the  top,  and  sounded  automatically  by 
the  action  of  the  sea,  on  the  passage  of  any  wave  or  undula- 
tion, which  will  cause  the  instrument  to  rise  and  fall  six 
inches  or  more.  It  will  emit  a  sound  that  can  be  heard  dis- 
tinctly from  one  to  fifteen  miles, — a  mournful  sound,  which, 
though  of  great  aid  to  navigation,  is  most  obnoxious  to  those 
who  live  within  ear-shot.  They  can  be  used  on  shoals,  where 
a  light-ship  is  needed  but  could  not  live  ;  and  are  well  suited 
for  broken  and  turbulent  waters,  as  the  rougher  the  sea  the 
louder  their  sound  :  they  are  also  employed  for  roadsteads 
and  the  open  sea. 

The  Bell-buoy  consists  of  a  buoy  with  a  bell  so  attached 
that  it  will  cause  the  bell  to  strike  as  the  buoy  is  moved  from 
side  to  side  by  the  action  of  the  sea.  Like  the  whistling-buoy, 
the  bell-buoy  sounds  the  loudest  when  the  sea  is  roughest,  but 
is  adapted  to  shoal  water,  where  the  whistling-buoy  could  not 
ride.  It  is  preferred  for  harbors,  rivers,  and  other  places 
where  the  sound  range  needed  is  short. 


BELL-BUOY, 


96  SIMPLE    ELEMENTS    Otf    NAVIGATION. 

Steam-whistles  for  signalling  in  a  fog  are  the  same  in- 
struments ordinarily  used  on  steamboats  and  locomotives. 
They  have  been  heard  at  distances,  varying  with  their  diame- 
ter, of  from  three  to  twenty-five  miles. 

The  Trumpet  comes  next  in  order,  and  is  simply  a  horn 
that  is  capable  of  making  shrieks  which  can  be  heard  at  a 
great  distance,  and  is  superior  to  the  whistle,  having  greater 
penetrating  effect. 

The  Siren  is  beyond  all  doubt  the  most  powerful  fog-signal 
in  use,  and  when  operated  under  a  pressure  of  seventy  pounds 
of  steam  can  be  heard,  under  favorable  circumstances,  from 
twenty  to  thirty  miles.  Its  density,  pitch,  and  penetration 
render  it  dominant  over  noises  after  all  other  signal  sounds 
have  succumbed,  especially  under  meteorological  conditions 
unfavorable  to  the  transmission  of  sound. 

The  trumpet,  siren,  and  whistle  are  capable  of  such  arrange- 
ment that  the  length  of  blast  and  interval  and  the  succession 
of  alternating  are  such  as  to  identify  the  location  of  each,  so 
that  the  position  may  be  determined  by  the  sound.  Double 
sirens  of  different  pitch  are  sometimes  used.  There  are  in 
addition  to  these,  in  various  parts  of  the  world,  several  sound- 
signals  made  by  utilizing  natural  orifices  in  cliffs,  through 
which  the  waves  drive  the  air  in  such  force  and  velocity  as  to 
produce  the  sound  required. 

Sound-signals  constitute  a  large  factor  in  the  safety  of  navi- 
gation, and  it  is  necessary  that  every  signal  should  have  its 
own  characteristic  to  particularly  indicate  itself,  as  a  light- 
house is  made  to  proclaim  its  own  individuality  by  some 
distinguishing  feature.  The  effect  of  different  atmospheric 
conditions  upon  the  transmission  of  sound  is  very  marked, 
and  it  has  been  found  by  repeated  trials  that  the  sound  range 
varies  on  clear,  calm  days;  hence  the  minimum  range  should 
always  be  taken  as  the  guide  when  running  by  sound.  A 
most  important  phenomenon,  affording  confidence  in  sound- 
signalling  when  a  light  is  rendered  ineffectual,  is  the  fact  that 
a  foggy  atmosphere  appears  to  be  a  highly  favorable  condi- 
tion for  the  transmission  of  sound;  while  rain,  hail,  and  snow 
offer  no  obstruction,  but,  on  the  contrary,  have  the  effect  of 
assisting  the  passage  of  sound. 

It  will  be  seen  from  the  above  that  a  vessel  coming  to  the 
coast  from  beyond  the  sea  will  pick  up  the  proper  coast-light 


AIDS  TO   NAVIGATION". 


97 


02 
H 

fi 


98  SIMPLE    ELEMENTS   OF   NAVIGATION. 

in  fair  weather,  and  in  thick  weather  the  fog-signal,  and  take 
either  as  a  point  of  departure  and  feel  the  way  to  the  harbor 
light  or  fog-signal  in  the  port,  thence  to  a  safe  anchorage, 
with  comparative  security. 


CHAPTER  XI. 
REGULATIONS  FOR  PREVENTING  COLLISIONS  AT  SEA. 

THE  laws  of  all  Maritime  Nations  require  a  strict  observance 
of  the  following  rules  and  regulations  for  the  prevention  of 
collisions  at  sea. 

"  ART.  1.  In  the  following  rules  every  steamship  which  is 
under  sail  and  not  under  steam  is  to  be  considered  a  sailing- 
ship,  and  every  steamship  which  is  under  steam,  whether  un- 
der sail  or  not,  is  to  be  considered  a  ship  under  steam. 

"  RULES  CONCERNING  LIGHTS. 

"ART.  2.  The  lights  mentioned  in  the  following  articles 
numbered  three,  four,  five,  six,  seven,  eight,  nine,  ten,  and 
eleven,  and  no  others,  shall  be  carried  in  all  weathers,  from  sun- 
set to  sunrise. 

"ART.  3.  A  sea-going  steamship,  when  under  way,  shall 
carry — 

"  (a)  On  or  in  front  of  the  foremast,  at  a  height  above  the 
hull  of  not  less  than  twenty  feet,  and  if  the  breadth  of  the 
ship  exceeds  twenty  feet,  then  at  a  height  above  the  hull  not 
less  than  such  breadth,  a  bright  white  light,  so  constructed  as 
to  show  a  uniform  and  unbroken  light  over  an  arc  of  the  hori- 
zon of  twenty  points  of  the  compass,  so  fixed  as  to  throw  the 
light  ten  points  on  each  side  of  the  ship,  namely,  from  right 
ahead  to  two  points  abaft  the  beam  on  either  side,  and  of  such 
a  character  as  to  be  visible  on  a  dark  night,  with  a  clear  atmos- 
phere, at  a  distance  of  at  least  five  miles. 

"  (b)  On  the  starboard  side  a  green  light,  so  constructed  as 
to  show  a  uniform  and  unbroken  light  over  an  arc  of  the  hori- 
zon of  ten  points  of  the  compass,  so  fixed  as  to  throw  the  light 
from  right  ahead  to  two  points  abaft  the  beam  on  the  starboard 


REGULATIONS   FOR   PREVENTING    COLLISION'S.      99 

side,  and  of  such  a  character  as  to  be  visible  on  a  dark  night, 
with  a  clear  atmosphere,  at  a  distance  of  at  least  two  miles. 

"  (c)  On  the  port  side  a  red  light,  so  constructed  as  to  show  a 
uniform  and  unbroken  light  over  an  arc  of  the  horizon  of  ten 
points  of  the  compass,  so  fixed  as  to  throw  the  light  from 
right  ahead  to  two  points  abaft  the  beam  on  the  port  side,  and 
of  such  a  character  as  to  be  visible  on  a  dark  night,  with  a 
clear  atmosphere,  at  a  distance  of  at  least  two  miles. 

"  (d)  The  said  green  and  red  side-lights  shall  be  fitted  with 
inboard  screens  projecting  at  least  three  feet  forward  from  the 
light,  so  as  to  prevent  these  lights  from  being  seen  across  the 
bow. 

"ART.  4.  A  steamship  when  towing  another  ship  shall,  in 
addition  to  her  side-lights,  carry  two  bright  white  lights  in  a 
vertical  line,  one-over  the  other,  not  less  than  three  feet  apart, 
so  as  to  distinguish  her  from  other  steamships.  Each  of  these 
lights  shall  be  of  the  same  construction  and  character,  and 
shall  be  carried  in  the  same  position,  as  the  white  light  which 
other  steamships  are  required  to  carry. 

"ART.  5.  (a)  A  ship,  whether  a  steamship  or  a  sailing-ship, 
which  from  any  accident  is  not  under  command,  shall  at  night 
carry,  in  the  same  position  as  the  white  light  which  steamships 
are  required  to  carry,  and  if  a  steamship,  in  place  of  that  light, 
three  red  lights  in  globular  lanterns,  each  not  less  than  ten 
inches  in  diameter,  in  a  vertical  line,  one  over  the  other,  not 
less  than  three  feet  apart,  and  of  such  a  character  as  to  be  vis- 
ible on  a  dark  night,  with  a  clear  atmosphere,  at  a  distance 
of  at  least  two  miles,  and  shall  by  day  carry  in  a  vertical  line, 
one  over  the  other,  not  less  than  three  feet  apart,  in  front  of 
but  not  lower  than  her  foremast-head,  three  black  balls  or 
shapes,  each  two  feet  in  diameter. 

"  (b)  A  ship,  whether  a  steamship  or  a  sailing-ship,  em- 
ployed in  laying  or  in  picking  up  a  telegraph  cable,  shall  at 
night  carry,  in  the  same  position  asa  white  light  which  steam- 
ships are  required  to  carry,  and  if  a  steamship,  in  place  of  that 
light,  three  lights  in  globular  lanterns,  each  not  less  than  ten 
inches  in  diameter,  in  a  vertical  line,  over  one  another,  not  less 
than  six  feet  apart.  The  highest  and  lowest  of  these  lights  shall 
be  red,  and  the  middle  light  shall  be  white,  and  they  shall  be 
of  such  a  character  that  the  red  lights  shall  be  visible  at  the 
same  distance  as  the  white  light.  By  day  she  shall  carry,  in  a 


100  SIMPLE    ELEMENTS    OF    NAVIGATION. 

vertical  line,  one  over  the  other,  not  less  than  six  feet  apart, 
in  front  of  but  not  lower  than  her  foremast  head,  three  shapes 
not  less  than  two  feet  in  diameter,  of  which  the  top  and 
bottom  shall  be  globular  in  sphae  and  red  in  color,  and  the 
middle  one  diamond  in  shape  and  white. 

"(c)  The  ships  referred  to  in  this  article  when  not  making 
any  way  through  the  water  shall  not  carry  the  side-lights,  but 
when  making  way  shall  carry  them. 

"(d)  The  lights  and  shapes  required  to  be  shown  by  this 
article  are  to  be  taken  by  other  ships  as  signals  that  the  ship 
showing  them  is  not  under  command,  and  cannot  therefore 
get  out  of  the  way.  The  signals  to  be  made  by  ships  in  dis- 
tress and  requiring  assistance  are  contained  in  article  twenty- 
seven. 

"ART.  6.  A  sailing-ship  under  way  or  being  towed  shall 
carry  the  same  lights  as  are  provided  by  article  three  for  a 
steamship  under  way,  with  the  exception  of  the  white  light, 
which  she  shall  never  carry. 

"  ART.  7.  Whenever,  as  in  the  case  of  small  vessels  during 
bad  weather,  the  green  and  red  side-lights  cannot  be  fixed, 
these  lights  shall  be  kept  on  deck,  on  their  respective  sides  of 
the  vessel,  ready  for  use,  and  shall,  on  the  approach  of  or  to 
other  vessels,  be  exhibited  on  their  respective  sides  in  suffi- 
cient time  to  prevent  collision,  in  such  manner  as  to  make 
them  most  visible,  and  so  that  the  green  light  shall  not  be  seen 
on  the  port  side  nor  the  red  light  on  the  starboard  side.  To 
make  the  use  of  these  portable  lights  more  certain  and  easy, 
the  lanterns  containing  them  shall  each  be  painted  outside 
with  the  color  of  the  light  they  respectively  contain,  and  shall 
be  provided  with  proper  screens. 

"ART.  8.  A  ship,  whether  a  steamship  or  a  sailing-ship, 
when  at  anchor,  shall  carry,  where  it  can  best  be  seen,  but  at 
a  height  not  exceeding  twenty  feet  above  the  hull,  a  white 
light,  in  a  globular  lantern  of  not  less  than  eight  inches  in 
diameter,  and  so  constructed  as  to  show  a  clear,  uniform,  and 
unbroken  light,  visible  all  round  the  horizon  at  a  distance  of 
at  least  one  mile. 

"ART.  9.  A  pilot  vessel,  when  engaged  on  her  station  on 
pilotage  duty,  shall  not  carry  the  lights  required  for  other 
vessels,  but  shali*carry  a  white  light  at  the  mast-head,  visible 
all  round  the  horizon,  and  shall  also  exhibit  a  flare-up  light 


REGULATIONS    I'Oli    I'KEY  EXTlNU    COLLISIONS.    lUl 

or  flare-up  lights  at  short  intervals,  which  shall  never  exceed 
fifteen  minutes.  A  pilot  vessel,  when  not  engaged  on  her 
station  on  pilotage  duty,  shall  carry  lights  similar  to  those  of 
other  ships. 

"ART.  10.  Open  boats  and  fishing- vessels  of  less  than 
twenty  tons  net  registered  tonnage,  when  under  way  and  not 
when  having  their  nets,  trawls,  dredges,  or  lines  in  the  water, 
shall  not  be  obliged  to  carry  the  colored  side-lights  ;  but  every 
such  boat  and  vessel  shall  in  lieu  thereof  have  ready  at  hand 
a  lantern  with  a  green  glass  on  the  one  side  and  a  red  glass  on 
the  other  side,  and  on  approaching  to  or  being  approached  by 
another  vessel  such  lantern  shall  be  exhibited  in  sufficient 
time  to  prevent  collision,  so  that  the  green  light  shall  not  be 
seen  on  the  port  side  nor  the  red  light  on  the  starboard  side. 

"The  following  portion  of  this  article  applies  only  to  fish- 
ing-vessels and  boats  when  in  the  sea  off  the  coast  of  Europe 
lying  north  of  Cape  Fiuisterre  : 

"  (a)  All  fishing-vessels  and  fishing-boats  of  twenty  tons  net 
registered  tonnage  or  upward,  when  under  way  and  when  not 
having  their  nets,  trawls,  dredges,  or  lines  in  the  water,  shall 
carry  and  show  the  same  lights  as  other  vessels  under  way. 

"(6)  All  vessels  when  engaged  in  fishing  with  drift-nets 
shall  exhibit  two  white  lights  from  any  part  of  the  vessel 
where  they  can  be  seen.  Such  lights  shall  be  placed  so  that 
the  vertical  distance  between  them  shall  not  be  less  than  six 
feet  and  not  more  than  ten  feet,  and  so  that  the  horizontal 
distance  between  them,  measured  in  a  line  with  the  keel  of 
the  vessel,  shall  be  not  less  than  five  feet  and  not  more  than 
ten  feet.  The  lower  of  these  two  lights  shall  be  the  more 
forward,  and  both  of  them  shall  be  of  such  a  character  and 
contained  in  lanterns  of  such  construction  as  to  show  all 
round  the  horizon,  on  a  dark  night,  with  a  clear  atmosphere, 
for  a  distance  of  not  less  than  three  miles. 

"(c)  All  vessels  when  trawling,  dredging,  or  fishing  with 
any  kind  of  drag-nets  shall  exhibit,  from  some  part  of  the 
vessel  where  they  can  be  best  seen,  two  lights.  One  of  these 
lights  shall  be  red  and  the  other  shall  be  white.  The  red 
light  shall  be  above  the  white  light,  and  shall  be  at  a  vertical 
distance  from  it  of  not  less  than  six  feet  and  not  more  than 
twelve  feet ;  and  the  horizontal  distance  between  them,  if  any, 
shall  not  be  more  than  ten  feet.  These  two  lights  shall  be  of 


102  SIMPLE   ELEMENTS   OF   NAVIGATION. 

such  a  character  and  contained  in  lanterns  of  such  construc- 
tion as  to  be  visible  all  round  the  horizon,  on  a  dark  night, 
with  a  clear  atmosphere,  the  white  light  to  a  distance  of  not 
less  than  three  miles  and  the  red  light  of  not  less  than  two 
miles. 

"  (d)  A  vessel  employed  in  line-fishing,  with  her  lines  out, 
shall  carry  the  same  lights  as  a  vessel  when  engaged  in  fish- 
ing with  drift-nets. 

"  (e)  If  a  vessel  when  fishing  with  a  trawl,  dredge,  or  any 
kind  of  drag-net,  becomes  stationary  in  consequence  of  her 
gear  getting  fast  to  a  rock  or  other  obstruction,  she  shall  show 
the  light  and  make  the  fog-signal  for  a  vessel  at  anchor. 

"  (f)  Fishing- vessels  and  open  boats  may  at  any  time  use  a 
flare-up  in  addition  to  the  lights  which  they  are  by  this  arti- 
cle required  to  carry  and  show.  All  flare-up  lights  exhibited 
by  a  vessel  when  trawling,  dredging,  or  fishing  with  any  kind 
of  drag-net  shall  be  shown  at  the  af terpart  of  the  vessel,  ex- 
cepting that  if  the  vessel  is  hanging  by  the  stern  to  her  trawl, 
dredge,  or  drag-net  they  shall  be  exhibited  from  the  bow. 

"  (g)  Every  fishing-vessel  and  every  open  boat  when  at  an- 
chor between  sunset  and  sunrise  shall  exhibit  a  white  light, 
visible  all  round  the  horizon  at  a  distance  of  at  least  one  mile. 

"  (li)  In  a  fog  a  drift-net  vessel  attached  to  her  nets,  and  a 
vessel  when  trawling,  dredging,  or  fishing  with  any  kind  of 
drag-net,  and  a  vessel  employed  in  line-fishing  with  her  lines 
out,  shall,  at  intervals  of  not  more  than  two  minutes,  make  a 
blast  with  her  fog-horn,  and  ring  her  bell  alternately." 

Attention  is  called  to  paragraphs  "  a  "  and  "  c  "  of  this  ar- 
ticle, which  have  not  been  adopted  by  foreign  governments. 

Paragraph  "a"  has  been  modified  by  the  British  Govern- 
ment to  read  as  follows,  viz.- 

"  All  fishing  vessels  and  fishing-boats  of  twenty  tons  net 
registered  tonnage  or  upwards,  when  under  way  and  when 
not  required  by  the  following  regulations  in  this  article  to 
carry  and  show  the  lights  therein  named,  shall  carry  and  show 
the  same  lights  as  oilier  vessels  under  way." 

Paragraph  "  c"  has  been  omitted. 

But  these  two  provisions  apply  only  to  "  fishing-vessels  and 
boats  when  in  the  sea  off  the  coast  of  Europe  lying  north  of 
Cape  Fiuisterre." 

"  ART.  11.  A  ship  which   is  being  overtaken  by  another 


REGULATIONS   FOK    PREVENTING   COLLISIONS.    103 

shall  show  from  her  stern  to  such  last-mentioned  ship  a  white 
light  or  a  flare-up  light. 

"  SOUND  SIGNALS   FOR  FOG,    AND   SO   FORTH. 

"ART.  12.  A  steamship  shall  be  provided  with  a  steam- 
whistle  or  other  efficient  steam  sound-signals,  so  placed  that 
the  sound  may  not  be  intercepted  by  any  obstructions,  and 
with  an  efficient  fog-horn,  to  be  sounded  by  a  bellows  or  other 
mechanical  means,  and  also  with  an  efficient  bell.  (In  all 
cases  where  the  regulations  require  a  bell  to  be  used,  a  drum 
will  be  substituted  on  board  Turkish  vessels.)  A  sailing-ship 
shall  be  provided  with  a  similar  fog-horn  and  bell. 

"In  fog,  mist,  or  falling  snow,  whether  by  day  or  night, 
the  signals  described  in  this  article  shall  be  used  as  follows, 
that  is  to  say  : 

"  (a)  A  steamship  under  way  shall  make  with  her  steam- 
whistle  or  other  steam  sound-signal,  at  intervals  of  not  more 
than  two  minutes,  a  prolonged  blast. 

"  (b)  A  sailing-ship  under  way  shall  make  with  her  fog- 
horn, at  intervals  of  not  more  than  two  minutes,  when  on  the 
starboard  tack  one  blast,  when  on  the  port  tack  two  blasts  in 
succession,  and  when  with  the  wind  abaft  the  beam  three 
blasts  in  succession. 

"  (c)  A  steamship  and  a  sailing-ship  when  not  underway 
shall,  at  intervals  of  not  more  than  two  minutes,  ring  the  bell. 


( < 


SPEED    OF   SHIPS   TO   BE   MODERATE   IN   FOG,  AND   SO  FORTH. 


"ART.  13.  Every  ship,  whether  a  sailing-ship  or  a  steam- 
ship, shall  in  a  fog,  mist,  or  falling  snow  go  at  a  moderate 
speed. 

"  STEERING  AND   SAILING  RULES. 

"ART.  14.  When  two  sailing-ships  are  approaching  one 
another  so  as  to  involve  risk  of  collision,  one  of  them  shall 
keep  out  of  the  way  of  the  other  as  follows,  namely  : 

"  (a)  A  ship  which  is  running  free  shall  keep  out  of  the  way 
of  a  ship  which  is  close-hauled. 

"  (b)  A  ship  which  is  close-hauled  on  the  port  tack  shall  keep 
~ut  of  the  way  of  a  ship  which  is  close-hauled  on  the  starboard 
tack. 


104  SIMPLE    ELEMENTS   OF   KAVIGATIOH. 

"  (c)  When  both  are  running  free,  with  the  wind  on  differ- 
ent sides,  the  ship  which  has  the  wind  on  the  port  side  shall 
keep  out  of  the  way  of  the  other. 

"  (d)  When  both  are  running  free,  with  the  wind  on  the 
same  side,  the  ship  which  is  to  windward  shall  keep  out  of  the 
way  of  the  ship  which  is  to  leeward. 

"  (e)  A  ship  which  has  the  wind  aft  shall  keep  out  of  the 
way  of  the  other  ship. 

"  ART.  15.  If  two  ships  under  steam  are  meeting  end  on,  or 
nearly  end  on,  so  as  to  involve  risk  of  collision,  each  shall 
alter  her  course  to  starboard,  so  that  each  may  pass  on  the  port 
side  of  the  other.  This  article  only  applies  to  cases  where 
ships  are  meeting  end  on,  or  nearly  end  on,  in  such  a  manner 
as  to  involve  risk  of  collision,  and  does  not  apply  to  two  ships 
which  must,  if  both  keep  on  their  respective  courses,  pass  clear 
of  each  other.  The  only  cases  to  which  it  does  apply  are 
when  each  of  the  two  ships  is  end  on,  or  nearly  end  on,  to  the 
other  ;  in  other  words,  to  cases  in  which  b}r  day  each  ship  sees 
the  masts  of  the  other  in  a  line,  or  nearly  in  a  line,  with  her 
own,  and  by  night  to  cases  in  which  each  ship  is  in  such  a 
position  as  to  see  both  the  side-lights  of  the  other.  It  does  not 
apply  by  day  to  cases  in  which  a  ship  sees  another  ahead  cross- 
ing her  own  course,  or  by  night  to  cases  where  the  red  light  of 
one  ship  is  opposed  to  the  red  light  of  the  other,  or  where  the 
green  light  of  one  ship  is  opposed  to  the  green  light  of  the 
other,  or  where  a  red  light  without  a  green  light,  or  a  green 
light  without  a  red  light,  is  seen  ahead,  or  where  both  green 
and  red  lights  are  seen  anywhere  but  ahead. 

"  ART.  16.  If  two  ships  under  steam  are  crossing  so  as  to 
involve  risk  of  collision,  the  ship  which  has  the  other  on  her 
own  starboard  side  shall  keep  out  of  the  way  of  the  other. 

"  ART.  17.  If  two  ships,  one  of  which  is  a  sailing-ship  and 
the  other  a  steamship,  are  proceeding  in  such  directions  as  to 
involve  risk  of  collision,  the  steamship  shall  keep  out  of  the 
way  of  the  sailing-ship. 

"ART.  18.  Every  steamship,  when  approaching  another 
ship  so  as  to  involve  risk  of  collision,  shall  slacken  her  speed, 
or  stop  and  reverse,  if  necessary. 

"ART.  19.  In  taking  any  course  authorized  or  required  by 
these  regulations,  a  steamship  under  way  may  indicate  that 


REGULATIONS   FOR  PREVENTING   COLLISIONS.    105 

course  to  any  other  ship  which  she  has  in  sight  by  the  follow- 
ing signals  on  her  steam- whistle,  namely  : 

"One  short  blast  to  mean  'I  am  directing  my  course  to 
starboard. ' 

' '  Two  short  blasts  to  mean  '  I  am  directing  my  course  to 
port.' 

"  Three  short  blasts  to  mean  '  I  am  going  full  speed  astern.' 

"  The  use  of  these  signals  is  optional,  but  if  they  are  used 
the  course  of  the  ship  must  be  in  accordance  with  the  signal 
made. 

"ART.  20.  Notwithstanding  anything  contained  in  any  pre- 
ceding article,  every  ship,  whether  a  sailing-ship  or- a  steam- 
ship, overtaking  any  other  shall  keep  out  of  the  way  of  the 
overtaken  ship. 

"  ART.  21.  In  narrow  channels  every  steamship  shall,  when 
it  is  safe  and  practicable,  keep  to  that  side  of  the  fairway  or 
mid-channel  which  lies  on  the  starboard  side  of  such  ship. 

"ART.  22.  Where  by  the  above  rules  one  of  two  ships  is  to 
keep  out  of  the  way,  the  other  shall  keep  her  course. 

"ART.  23.  In  obeying  and  construing  these  rules  due  regard 
shall  be  had  to  all  dangers  of  navigation,  and  to  any  special 
circumstances  which  may  render  a  departure  from  the  above 
rules  necessary  in  order  to  avoid  immediate  danger. 


"NO   SHIP,  UNDER   ANY   CIRCUMSTANCES,  TO  NEGLECT  PROPER 

PRECAUTIONS. 

"ART.  24.  Nothing  in  these  rules  shall  exonerate  any  ship, 
or  the  owner,  or  master,  or  crew  thereof,  from  the  consequences 
of  any  neglect  to  carry  lights  or  signals,  or  of  any  neglect  to 
keep  a  proper  lookout,  or  of  the  neglect  of  any  precaution 
which  may  be  required  by  the  ordinary  practice  of  seamen  or 
by  the  circumstances  of  the  case. 


"RESERVATION  OF  RULES  FOR  HARBOR  AND  INLAND  NAVIGA- 
TION. 

"ART.  25.  Nothing  in  these  rules  shall  interfere  with  the 
operation  of  a  special  rule,  duly  made  by  local  authority, 
relative  to  the  navigation  of  any  harbor,  river,  or  inland  navi- 
gation. 


106  SIMPLE   ELEMENTS   OF   NAVIGATION. 

"SPECIAL  LIGHTS  FOR  SQUADRONS  AND  CONVOYS. 

"ART.  26.  Nothing  iii  these  rules  shall  interfere  with  the 
operation  of  any  special  rules  made  by  the  Government  of  any 
nation  with  respect  to  additional  station  and  signal  lights  for 
two  or  more  ships  of  war  or  for  ships  sailing  under  convoy. 

"ART.  27.  When  a  ship  is  in  distress  and  requires  assistance 
from  other  ships  or  from  the  shore,  the  following  shall  be  the 
signals  to  be  used  or  displayed  by  her,  either  together  or 
separately,  that  is  to  say  : 

"In  the  daytime— 

"First.  A  gun  fired  at  intervals  of  about  a  minute. 

"  Second.  The  international  code  signal  of  distress  indicated 
by  N.  C. 

"  Third.  The  distant  signal,  consisting  of  a  square  flag, 
having  either  above  or  below  it  a  ball,  or  anything  resembling 
a  ball. 

"  At  night— 

"  First.  A  gun  fired  at  intervals  of  about  a  minute. 

"Second.  Flames  on  the  ship  (as  from  a  burning  tar- barrel, 
oil-barrel,  and  so  forth). 

"Third.  Rockets  or  shells,  throwing  stars  of  any  color  or 
description,  fired  one  at  a  time,  at  short  intervals." 


TABLES. 


EXPLANATION  OF   TABLES. 


Table  I  contains  the  difference  of  latitude  and  departure 
corresponding  to  distances  not  exceeding  300  miles,  and  for 
courses  to  every  degree  of  the  compass. 

The  manner  of  using  this  table  is  explained  in  the  different 
problems  of  dead-reckoning. 

Table  II  gives  the  refraction,  dip  of  the  horizon,  and  the 
sun's  parallax  in  altitude;  the  application  of  these  is  explained 
in  the  text  under  the  definition  of  each  on  page  39. 

Table  III  gives  the  declination  of  the  sun  to  the  nearest 
minute  for  every  noon  at  Greenwich  from  the  year  1886  to 
1901,  and  this  table  will  answer  for  some  years  beyond  that 
period,  without  any  material  error.  This  declination  may  be 
reduced  to  any  other  meridian  in  the  following  manner:  Take 
from  the  table  the  declination  of  the  same  date  as  the  local 
date  and  mark  it  -f-  when  north  and  -  -  when  south,  and  ap- 
ply a  correction  equal  to  the  "  difference  for  one  hour,"  mul- 
tiplied by  the  hours  and  part  of  an  hour  of  the  longitude, 
adding  or  subtracting  the  correction  as  the  sign  in  the  table 
indicates;  for  a  time  after  noon  if  the  longitude  is  west,  for  a 
time  before  noon  if  the  longitude  is  east. 

EXAMPLE.     At  a  place  in  longitude  81°  15'  W.  on  April  15, 
1887,  find  the  declination.     Longitude  81°  15'  W.  =  -f  5". 42. 
Table  III.     Dec.  +  9°  45'          Diff.  one  hour  +    54" 
Corr.  for  -f  5h  42  -f-        4  53  Long,  -f-      5.42 

Declination  -f-  9  49  53  -f  292.68 

Corr.  +  4'  53" 

Had  this  longitude  been  east,  we  should  get,  longitude  81 
15'  E.  =  -  -  5h.42. 

Table  III.     Dec.  -f  9°  45'         Diff.  one  hour  +  54" 
Corr.  for  —  5h.42  —         4  53  Long.  -    5.42 


Declination  -f  9  40  07  -  292.68 

Corr.  -  -  4'  53" 
109 


110  EXPLANATION    OF   TABLES. 

To  find  the  declination  for  a  given  mean  time  at  a  given 
place  proceed  as  follows:  From  the  given  mean  time  find  the 
astronomical  time,  and  the  corresponding  Greenwich  date. 
Take  from  the  table  the  declination  for  the  nearest  preceding 
mean  time  date,  and  the  corresponding  difference  for  one 
hour,  noting  the  sign  of  each.  Multiply  the  difference  for 
one  hour  by  the  hours  and  parts  of  an  hour  of  the  remaining 
Greenwich  time,  and  apply  the  correction  according  to  the 
signs,  adding  if  they  are  alike,  and  subtracting  if  they  are 
unlike.  If  the  given  Greenwich  time  is  nearer  a  following 
than  a  preceding  date,  it  may  be  convenient  to  interpolate 
back  from,  the  following  date. 

EXAMPLE.  At  a  given  place  in  longitude  81°  15'  W.  on 
April  15,  1887,  10  A.M.,  find  the  declination. 

Local  astronomical  time  14d  22h  00m 

Longitude  -|-     5   25 
Greenwich  mean  time  15     3   25 

Table  III.        Dec.  -f-  9°  45'       Diff.  one  hour  -f     54" 

Corr.  for  G.  M.  T.  -f        3.03       G.  M.  Time  -f 3.4 

Declination  +  9   48.03  4-   186.6 

Corr.  +  3'  03" 

Table  IV  contains  the  equation  of  time  for  every  noon  at 
Greenwich,  and  is  to  be  reduced  to  any  other  hour  by  means 
of  Table  IV«.  Thus,  suppose  the  equation  of  time  was  re- 
quired for  Feb.  21,  1888,  at  10  A.M.,  corresponding  to  Feb. 
20th,  22  hours,  Table  IV  gives  the  equation  of  time  for  Feb. 
20th,  14m  00s,  and  for  the  21st,  13m  53s;  the  difference  between 
the  two  is  a  daily  decrease  of  7s.  Now  enter  Table  IV«,  and 
with  7  at  the  top  and  22  at  the  side,  the  corresponding  6  in 
the  column  is  the  number  of  seconds  to  subtract  from  14m  00s 
to  give  the  required  equation  of  time,  13'"  54s.  This  6  seconds 
would  have  been  added  had  the  equation  of  time  been  increas- 
ing. The  equation  of  time  thus  found  is  to  be  applied  to  the 
apparent  time,  as  stated  at  the  head  of  the  column  in  Table  IV. 
To  obtain  the  apparent  time  from,  the  mean  time,  the  equation 
of  time  is  applied  opposite  to  the  heading  in  Table  IV. 

Table  V  contains  the  quantities  that  are  convenient  for 
finding  the  time,  or  the  total  error  of  the  compass,  by  an  alti- 
tude of  the  sun.  To  find  the  sine,  secant,  etc.,  for  the  de- 
grees, minutes,  and  seconds  of  the  date  occurring  in  the  prob- 
lems, look  for  the  degrees  at  the  bottom  of  the  page  when 


EXPLANATION    OF   TABLES.  Ill 

between  45°  and  135°,  otherwise  at  the  top,  the  minutes  being 
found  in  the  column  marked  M.,  which  stands  on  the  side  of 
the  page  on  which  the  degrees  are  marked;  and  if  the  degrees 
are  found  at  the  top,  the  names,  hour,  sine,  secant,  etc.,  must 
also  be  found  at  the  top;  and  if  the  degrees  are  found  at  the 
bottom,  the  names,  hour,  sine,  secant,  etc.,  must  be  found  at 
the  bottom.  Opposite  to  the  minutes  will  be  found  the  sine, 
secant,  etc.,  in  the  columns  marked  sine,  secant,  etc.,  respec- 
tively. Now,  with  the  number  of  seconds  in  the  left-hand 
column  under  M.,  take  out  the  number  in  the  nearest  column 
marked  "Diff.,"  which  add  to  the  sine,  secant,  etc.,  if  increas- 
ing, or  subtract  if  decreasing. 

Thus,  to  find  the  cosine  of  30°  20'  20",  with  30°  at  the  top  of 
the  page  and  opposite  to  20'  under  M.  in  the  column  marked 
cosine,  will  be  found  9.93606.  Now,  with  20"  in  the  left  col- 
umn of  M.,  we  find  opposite  in  the  nearest  column  of  "  Diff." 
the  figure  2  to  be  subtracted  from  the  cosine  as  it  is  decreas- 
ing, which  gives  the  correct  cosine,  9.93604.  Should  it  be 
desired  to  find  the  degrees,  minutes,  and  seconds  correspond- 
ing to  this  cosine,  we  search  in  the  column  of  cosines  for  the 
nearest  figures  to  those  given,  which  will  be  in  the  column 
under  30°,  and  opposite  to  the  nearest  number  in  the  column 
M.  corresponding  to  30,  will  be  found  20.  Take  the  differ- 
ence between  the  given  number  and  the  nearest  in  the  column, 
which  is  2.  Now,  with  this  2,  look  in  the  nearest  column  of 
"  Diff.,"  and  as  there  are  several  numbers  marked  2,  take  the 
middle  one,  opposite  to  which,  in  the  left-hand  column  under 
M.,  will  be  found  16  or  30°  20'  16",  sufficiently  near  for  all 
practicable  purposes. 

The  method  of  finding  the  hours,  minutes,  and  seconds  cor- 
responding to  the  sine,  etc.,  is  fully  given  in  the  text  on  find- 
ing the  longitude. 


TABLE  I. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE, 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  1°. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lnt. 

Dep. 

Dist 

Lat 

Dep. 

I 

1.0 

0.0 

61 

61.  o 

!_. 

121 

121.  0 

2.  I 

181 

181.0 

3-  2 

241 

241.0 

4-2 

2 

2.0 

o.  o 

62 

62.  o 

f. 

22 

122.  O 

2.  I 

82 

182.0 

3  2 

42 

242.  o 

4.2 

3 

3-0 

o. 

63 

63.  o 

I. 

23 

123.0 

2.  I 

83 

183.0 

3-2 

43 

243-0 

4.2 

4 

4.0 

0. 

64 

64.  o 

I. 

24 

124.  o 

2.  2 

84 

184.  o 

3-2 

44 

244.0 

4-3 

S 

5.  o 

o. 

65 

65.  o 

I. 

25 

125.  o 

2.  2 

85 

185.0 

3-2 

45 

245.0 

4-3 

5 

6.  o 

o. 

66 

66.0 

I.  2 

26 

126.  o 

2.  2 

86 

186.  o 

3-2 

46 

246".  o 

4-3 

7 

7.0 

o. 

67 

67.  o 

1.2 

27 

127.  o 

2.  2 

87 

187.0 

3-3 

47 

247.0 

4-3 

8 

8.0 

o. 

68 

68.0 

I.  2 

28 

128.0 

2.2 

88 

188.0 

3-3 

48 

248.  o 

4-3 

9 

9.0 

O,  2 

69 

69.  o 

I.  2 

29 

129.0 

2-3 

89 

189.  o 

3-3 

49 

249.0 

4-3 

10 

lo.  o 

O.  2 

70 

70.  o 

1.2 

3° 

130.0 

2-3 

90 

190.  o 

3-3 

50 

250.  o 

4-4 

II 

II.  0 

O.  2 

71 

71.0 

1.  2 

131 

131.  o 

2-3 

191 

191.0 

3-3 

251 

251.  o 

4-4 

12 

12.0 

0.  2 

72 

72.0 

1-3 

32 

132.  o 

2.3 

92 

192.  o 

3-4 

52 

252.0 

4-4 

13 

13-0 

0.  2 

73 

73-o 

I.  3 

33 

133-0 

2.3 

93 

193.0 

3-4 

53 

253.0 

4-4 

'4 

14.  o 

O.  2 

74 

74.0 

1-3 

34 

134.0 

2-3 

94 

194.0 

3-4 

54 

254.0 

4-4 

15 

15.  o 

0-3 

75 

75.o 

i-3 

35 

135-0 

2.4 

95 

195.0 

3-4 

55 

255.0 

4-5 

16 

16.  o 

76 

70.  o 

'•3 

36 

136.  o 

2-4 

96 

196.  o 

3-4 

56 

256.  o 

4-5 

17 

17.0 

°.  3 

77 

77.0 

i-3 

37 

137-0 

2.4 

97 

197.0 

3-4 

57 

257.0 

4-5 

18 

18.  o 

0-3 

78 

78.  o 

1.4 

38 

138.6 

2.  "4 

198.0 

3-5 

58 

258.0 

4-5 

'9 

19.0 

o.  3 

79 

79.0 

1.4 

39 

139.0 

2.4 

99 

199.0 

3-5 

59 

259.0 

4-5 

20 

20.  o 

o-3 

80 

80.0 

1.4 

40 

140.  o 

2.4 

200 

ICO.  O 

3-5 

60 

260.  o 

4-5 

21 

21.  O 

0.4 

Si 

81.0 

1.4 

141 

141.  o 

2-5 

201 

£OI.  O 

3-5 

261 

261.  o 

4.6 

22 

22.  O 

0.4 

82 

82.0 

1-4 

42 

142.  o 

2-5 

02 

202.  O 

3-5 

62 

262.  o 

4.6 

23 

23.0 

0.4 

83 

83.  o 

1.4 

43 

143.0 

2-5 

°3 

203.  o 

3-5 

°3 

263.  o 

4.6 

24 

24.  o 

0.4 

84 

84.0 

1-5 

44 

144.0 

2-5 

04 

204.  o 

3.6 

64 

264.  o 

4-6 

25 

25,O 

0.4 

85 

85.0 

1-5 

45 

145.0 

2-5 

°5 

205.  o 

3-6 

65 

265.  o 

4.6 

26 

26.  o 

86 

86.0 

i-S 

46 

146.0 

2.  5 

06 

206.  o 

3-6 

66 

266.  o 

4.6 

27 

27.0 

0.5 

87 

87.0 

47 

147.0 

2.6 

07 

207.  o 

3-6 

67 

267.  o 

4-7 

28 

28.0 

°-5 

88 

88.0 

i.  5 

48 

148.  o 

2.6 

08 

208.  o 

3-6 

68 

268.0 

4-7 

29 

29.  o 

0.5 

89 

89.0 

1.6 

49 

149.  o 

2.6 

09 

209.  o 

3-6 

69 

269.  o 

4-7 

3° 

30.  o 

0.5 

90 

90.  o 

1.6 

5° 

150.0 

2.  6 

10 

210.  O 

3-7 

7° 

270.0 

4-7 

3' 

31.0 

0.5 

91 

91.  o 

1.6 

IS' 

151.  o 

2.  6 

211 

211.  O 

3-7 

271 

271.0 

4-7 

32 

32.0 

0.6 

92 

92.  o 

1.6 

52 

152.  o 

2.7 

12 

212.  O 

3-7 

72 

272.  o 

4-  7 

33 

33-0 

0.6 

93 

93-0 

1.6 

53 

153.0 

2.7 

13 

213.0 

3-7 

73 

273.0 

4-8 

34 

34-0 

0.6 

94 

1.6 

54 

154.0 

2.7 

214.  o 

3-7 

74 

274.0 

4.8 

35 

35-° 

0.6 

95 

OS-0 

1-7 

55 

155-0 

2.7 

15 

215.0 

3-8 

75 

275.0 

4.8 

36 

36.0 

0.6 

96 

96.  o 

i.  7 

56 

156.  o 

2.7 

16 

216.  o 

3-8 

76 

276.  o 

4.8 

37 

37-0 

0.6 

97 

97-0 

i.  7 

57 

157.0 

2.7 

17 

217.0 

3-8 

77 

277.0 

4.8 

38 

38.0 

0.7 

98 

98.0 

1-7 

58 

158.0 

2.8 

18 

218,  O 

3-8 

78 

278.  o 

4-9 

39 

39-0 

0.7 

99 

C9-  o 

1-7 

59 

159.0 

2.8 

19 

219.0 

3-8 

79 

279.0 

4.9 

40 

40.  o 

0.7 

100 

loo.  o 

1-7 

60 

1  60.  0 

2.8 

20 

2  2O.  O 

3-8 

80 

280.0 

4-9 

4' 

41.  o 

0-7 

IOI 

IOI.  O 

i.H 

IOI 

IOI.  O 

2.  S 

221 

221.0 

3-9 

281 

281.0 

4-9 

42 

42.  o 

o.  7 

02 

IO2.  O 

1.8 

62 

162.0 

2.8 

22 

222.  O 

3-9 

82 

282.  o 

4-9 

43 

43-0 

0.8 

03 

103.  o 

1.8 

63 

163.  o 

2.8 

23 

223.0 

3-9 

83 

283.0 

4-9 

44 

44-0 

0.8 

04 

104  o 

1.8 

64 

164.  o 

2.9 

24 

224.  o 

3-9 

84 

284.0 

5.0 

45 

45.0 

0.8 

°5 

105.  o 

1.8 

65 

165.0 

2.9 

25 

225.  o 

3-9 

85 

285.0 

5-° 

46 

46.  o 

0.8 

06 

1  06.  O 

1.8 

66 

1  66.  o 

2.9 

26 

2:6.  o 

3-9 

86 

286.0 

47 

47.0 

0.8 

07 

107.  o 

1-9 

67 

167.0 

2.9 

27 

227.0 

4.0 

87 

287.0 

5-o 

48 

48.0 

0.8 

08 

1  08.  O 

1-9 

es 

168.0 

2.9 

28 

228.0 

4.0 

88 

288.0 

5.0 

49 

49.0 

0.9 

09 

109.  o 

1-9 

69 

169.  o 

2.9 

29 

229.  o 

4-0 

89 

289.  o 

5-0 

5° 

50.  o 

0-9 

10 

no.  o 

1.9 

70 

170.0 

3-0 

30 

230.  o 

4.0 

90 

290.  o 

5-1 

5r 

51.0 

0.9 

III 

III.  0 

1-9 

i?1 

171.0 

3-0 

231 

23I.O 

4.0 

291 

291.  o 

5- 

52 

52.0 

0.9 

12 

112.  O 

2.0 

72 

172.0 

3-  o 

32 

232.0 

4.0 

92 

292.  o 

5- 

53 

53-0 

0.9 

13 

113.0 

2.  0 

73 

173.0 

3-0 

33 

233.0 

4- 

93 

293.0 

5- 

54 

54-0 

0.9 

14 

114.  o 

2.  O 

74 

174.0 

3-0 

34 

234.  o 

4- 

94 

294.0 

5- 

55 

55-0 

.  o 

15 

115.0 

2.0 

75 

175.0 

3- 

35 

235-0 

4- 

95 

295.0 

5- 

56 

56.0 

.  o 

16 

116.  6 

2.  O 

76 

176.  o 

3- 

3° 

236.  o 

4- 

96 

296.  o 

5-2 

57 

57-0 

.0 

17 

117.0 

2.  0 

77 

177.0 

3- 

37 

237.0 

4- 

97 

297.0 

5-2 

58 

58.0 

.0 

18 

Mo.  O 

2.  I 

78 

178.0 

3- 

38 

238.0 

4-2 

98 

298.0 

5-2 

59 

59.0 

.0 

19 

119.0 

2.  1 

79 

179-0 

3- 

39 

239.  o 

4-2 

99 

299.  o 

5.2 

60 

60.0 

.0 

20 

120.  o 

2.  I 

80 

180.0 

3- 

40 

240.  o 

4-2 

300 

300.0 

5-2 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

[For  89  Degrees. 

114 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2°. 

Dlst 

Lat. 

Dep. 

Dlst 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

I 

I.  O 

O.  0 

61 

61.0 

2.  I 

121 

120.  9 

4-2 

iSi 

180.9 

6-3 

241 

240.9 

8.4 

2 

2.0 

0.  I 

62 

62.  o 

2.  2 

22 

121.  9 

4-3 

82 

181.9 

6.4 

42 

241.9 

8.4 

3 

3-" 

O.  I 

63 

63.  o 

2.  2 

23 

122.  9 

4-3 

83 

182.9 

6.4 

43 

242.9 

8.5 

4 

4.0 

0.  I 

64 

64.  o 

2.  2 

24 

123.9 

4-3 

84 

183.9 

6.4 

44 

243-9 

8.5 

I 

5.  o 
6.0 

O.  2 
O.  2 

65 
66 

65.0 
66.0 

2-3 
2-3 

20 

124.9 
125.9 

4-4 
4.4 

85 
86 

184.9 
185.9 

<"5 
6.5 

45 
46 

244.9 
245.9 

8.6 
8.6 

7 

7-° 

O.  2 

67 

67.  o 

2-3 

27 

126.9 

4-4 

S7 

186.9 

6-5 

47 

246.  8 

8.6 

8 

8.0 

0-3 

68 

68.0 

2.4 

28 

127.9 

4-5 

88 

187.9 

6.6 

48 

247.8 

8-7 

9 

9.0 

°-3 

69 

69.  o 

2.4 

29 

128.9 

4-5 

89 

188.9 

6.6 

49 

248.8 

8.7 

10 

IO.  O 

°-3 

7° 

70.  o 

2.4 

3° 

129.9 

4-5 

9° 

189.9 

6.6 

50 

249.8 

8-7 

il 

II.  O 

0.4 

7i 

71.0 

2-5 

131 

130.9 

4.6 

191 

190.9 

6.7 

251 

250.8 

8.8 

12 

12.  0 

0.4 

72 

72.0 

2-5 

32 

J3I-9 

4.6 

92 

191.9 

6.7 

52 

251.8 

8.8 

'3 

13-0 

0.5 

73 

73-° 

2-5 

33 

i32-9 

4-6 

93 

192.9 

6-7 

S3 

252.8 

8.8 

«4 

14-0 

0.5 

74 

74-o 

2.6 

34 

'33-9 

4-7 

94 

193-9 

6.8 

54 

253.8 

8.9 

15 

15.  o 

0.5 

75 

75.0 

2.6 

35 

134-9 

4-7 

95 

194.9 

6.8 

55 

254.8 

8.9 

16 

16.  o 

0.6 

7^ 

76.0 

2.7 

3° 

135-9 

4-  7 

96 

195-9 

6.8 

56 

255-8 

8.9 

17 

17.0 

0.6 

77 

77.0 

2.7 

37 

136.9 

4.8 

97 

196.9 

6.9 

57 

256.8 

9.0 

18 

18.  o 

0.6 

7» 

78.0 

2-7 

38 

137.9 

4.8 

98 

197-9 

6.9 

58 

257.8 

9.0 

19 

19.  o 

0.7 

79 

79.0 

2.8 

39 

138.9 

4-9 

99 

198.9 

6-9 

59 

258.8 

9.0 

20 

20.  O 

o.  7 

So 

80.0 

2.8 

40 

139-9 

4.9 

200 

199.9 

7-o 

60 

259.8 

9-1 

21 

21.  O 

0.7 

81 

81.0 

2.8 

141 

140.9 

4-9 

201 

200  9 

7.0 

261 

260.8 

9-1 

22 

22.0 

0.8 

82 

82.0 

2.9 

42 

141.9 

5-o 

O2 

201.  9 

7.0 

62 

261.8 

9-' 

23 

23  o 

0.8 

83 

82.9 

2.9 

43 

142.9 

5-0 

03 

2O2.  9 

7-i 

63 

262.8 

9.2 

24 

24.  o 

0.8 

84 

83-9 

2.9 

44 

143-9 

5-0 

04 

203.9 

7-1 

64 

263.8 

9.2 

25 

25.0 

0.9 

85 

84.9 

3-o 

45 

144.9 

5-1 

05 

204.9 

7.2 

65 

264.8 

9.2 

26 

27 

26.  o 
27.0 

0.9 
0.9 

86 
87 

85.9 
86.9 

3-0 

3-0 

46 

47 

145-9 
146.9 

5-i 

5-i 

06 
07 

205.9 

206.  9 

7-2 
7.2 

66 
67 

265.8 
266.8 

9-3 
9-3 

28 

28.0 

.  o 

£8 

87.9 

3-  i 

48 

147-9 

5-2 

08 

207.9 

7-3 

68 

267.8 

9.4 

29 

29.0 

.  o 

89 

88.9 

3-i 

49 

148.9 

5-2 

09 

208.  9 

7-3 

69 

268.8 

9-4 

3° 

30.  o 

.0 

90 

89.9 

3-  ' 

1° 

149.9 

5-2 

10 

209.9 

7-3 

7" 

269.  8 

9-4 

3' 

31.0 

.  I 

9' 

90.9 

3-2 

'5' 

150.9 

5-3 

211 

210.9 

7-4 

271 

270.8 

9-5 

32 

32.0 

.  I 

92 

91.9 

S-2 

52 

151.9 

5-3 

12 

211.  9 

7-4 

72 

271.8 

9-5 

33 

33-0 

.  2 

93 

92.9 

3-2 

53 

152.9 

5-3 

'3 

212.  9 

7-4 

73 

272.8 

9-5 

34 

34-  ° 

.  2 

94 

93-9 

3-3 

54 

'53-9 

5-4 

14 

213.9 

7-5 

74 

273.8 

9.6 

35 

35-o 

.2 

95 

94-9 

3-3 

55 

154-9 

5-4 

15 

214.9 

7-5 

75 

274.8 

9.6 

35 

36.  o 

•  3 

96 

95-9 

3-4 

5B 

'55-9 

5-4 

10 

215.  9 

7-5 

76 

275-8 

9-6 

37 

37-o 

•3 

97 

96.  o 

3-4 

57 

156.9 

5-5 

'7 

216.  9 

7.6 

77 

276.8 

9-7 

38 

38.0 

•  3 

98 

97-9 

3-4 

58 

'57-9 

5-5 

18 

217.9 

7-6 

78 

277.8 

9-7 

39 

39-0 

•  4 

99 

98.9 

3-5 

59 

158.9 

5-5 

'9 

218.9 

7.6 

P 

278.8 

9~l 

40 

40.  o 

•4 

IOO 

99-9 

3-5 

DO 

>59-9 

5-6 

20 

219.9 

7-7 

80 

279.8 

9.8 

41 

41.  o 

•4 

101 

100.  9 

3-5 

161 

1  60.  9 

5.6 

221 

220.  9 

7-7 

281 

280.8 

9.8 

42 

42.  o 

•  5 

02 

101.9 

3-6 

62 

161.9 

5-7 

22 

221.  9 

7-7 

82 

281.8 

9.8 

43 

43-0 

•  5 

°3 

102.  9 

3-6 

63 

162.  9 

5-7 

23 

222.  9 

7-8 

!3 

282.8 

9-9 

44 

44.0 

•  5 

04 

103-9 

3-6 

64 

163-9 

5-7 

24 

223.9 

7-8 

84 

283.8 

9-9 

45 

45.0 

.6 

05 

104.9 

3-7 

65 

164.9 

5-8 

25 

224.9 

7-9 

8s 

284.8 

9-9 

46 
47 

46.  o 
47-o 

.6 
.6 

06 
07 

105.9 
1  06.  9 

3-7 
3-7 

66 
67 

165.9 
1  66.  9 

5-8 
5.8 

26 

27 

225.9 

226.  9 

7-9 
7-9 

86 
87 

285.8 
286.8 

IO.  O 
IO.  O 

48 

49 

48.0 
49-o 

•  7 

.  7 

08 
09 

107.9 
1  08.  9 

r* 

68 

69 

167.9 
168.9 

5-9 
5-9 

28 
29 

227.  9 
228.  9 

8.0 
8.0 

88 
89 

287.8 
288.8 

IO.  I 

10.  I 

5° 

50.0 

•  7 

10 

109.9 

3-8 

7° 

169.9 

5-9 

3° 

220.  9 

8.0 

90 

280.8 

•  0.   I 

5' 

51.0 

.8 

III 

no.  9 

3-9 

i7« 

170.9 

6.0 

231 

230.9 

8.  ! 

291 

290.  8 

10.  2 

5- 

52.0 

.8 

12 

in.  9 

3-9 

72 

171-  9 

6.0 

32 

231.9 

8.1 

92 

291.8 

IO.  2 

53 

53-o 

.8 

'3 

112.9 

3-9 

73 

172.9 

6.0 

33 

232.9 

8.  i 

93 

292.  8 

IO.  2 

54 

54.0 

•  9 

14 

"3-9 

4.0 

74 

J73-9 

6.1 

34 

233-9 

8.2 

94 

293.8 

10.3 

55 

55-° 

•  9 

15 

114.9 

4.0 

75 

174-9 

6.1 

35 

234-9 

8.2 

95 

294-8 

10.3 

56 

56.0 

2.  O 

1  6 

115.9 

4.0 

76 

175-9 

6.  i 

36 

235-9 

8.2 

96 

295.8 

10.3 

57 

57.0 

2.  O 

'7 

1  16.  9 

4.1 

77 

176.9 

6.2 

37 

236.9 

8.3 

n 

296.  8 

10.  4 

58 

58.0 

2.  O 

18 

117.9 

4-  i 

78 

177-9 

6.2 

3« 

237-9 

8-3 

98 

297-8 

10.  4 

59 

59.0 

2.  I 

19 

118.9 

4-2 

79 

178.9 

6.2 

39 

238.9 

8-3 

99 

298.8 

10.  4 

60 

60.  o 

2.  I 

go 

119.9 

4-2 

80 

179-9 

6-3 

40 

239-9 

8.4 

300 

299.8 

10.5 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

DUt. 

Dep. 

Lat. 

DUt. 

Dep. 

Lat 

Dist. 

Dep. 

UU. 

[For  88  Degrees. 

115 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  3°. 

Dist 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

I 

I.O 

O.  I 

61 

60.  9 

3-  2 

121 

120.8 

6-3 

181 

180.  8 

9-5 

241 

240.  7 

12.6 

2 

2.  0 

O.  I 

62 

61.9 

3-2 

22 

121.  8 

6.4 

82 

181.8 

9-5 

42 

241.  7 

12.7 

3 

3-° 

0.  2 

63 

62.  9 

3-3 

23 

122.8 

6.4 

83 

182.  7 

9-6 

43 

242.7 

12.7 

4 

4.0 

0.  2 

64 

63.  9 

3-3 

24 

123.8 

6-5 

84 

183-7 

9.6 

44 

243-  7 

12.8 

I 

I'° 

6.  o 

°-3 

65 
66 

64.9 
65.9 

3-4 
3-5 

3 

124.8 
125.  8 

6-5 
6.6 

II 

184.7 
185.7 

9-7 
9-7 

45 
46 

244.  7 
245-  7 

12.8 

12.9 

7 

7.0 

0.4 

67 

06.  9 

3-5 

27 

126.8 

6.6 

87 

186.7 

9-8 

47 

246.7 

12.9 

8 

8.0 

0.4 

68 

67.9 

3-6 

28 

127.8 

6.7 

88 

187.7 

9.8 

48 

247-7 

"3-0 

9 

9,  o 

0.5 

69 

68.9 

3-6 

29 

128.8 

6.8 

89 

1  88.  7 

9-9 

49 

248.  7 

13-0 

IO 

IO.  O 

70 

69.9 

3-7 

.    3° 

129.8 

6.8 

90 

189-7 

9-9 

249.7 

'3-1 

II 

II.  0 

0.6 

7' 

70.9 

3-7 

131 

130.8 

6.9 

191 

190.7 

10.  O 

251 

250.7 

'3-' 

12 

12.0 

0.6 

72 

71.9 

3-8 

32 

131.  8 

6.9 

92 

191.  7 

IO.  O 

52 

251.7 

13 

13-0 

0.7 

73 

72.9 

3-8 

33 

132.8 

7.0 

93 

192.7 

IO.  I 

53 

252.7 

13-2 

14 

14.  o 

0.7 

74 

73-9 

3-9 

34 

133-8 

7-o 

94 

'93-7 

IO.  2 

54. 

253-7 

13-3 

IS 

15.0 

0.8 

75 

74-9 

3-9 

35 

134.8 

7-t 

95 

194-7 

10.  2 

55 

254.  7 

10 

16.0 

0.8 

76 

75-9 

4.0 

36 

135-8 

7-i 

96 

195-7 

10.3 

56 

255-6 

13-4 

17 

17.0 

0.9 

77 

76.9 

4.0 

37 

136.8 

7-2 

97 

196.  7 

10.3 

57 

256.6 

Z3-5 

18 

18.  o 

0.9 

78 

77-9 

4.  i 

3» 

137-8 

7-2 

98 

197-7 

io.  4 

58 

257.6 

13-5 

19 

19.0 

.  o 

79 

78.9 

4.  i 

39 

138.8 

7-3 

99 

198.7 

10.4 

59 

258.6 

13-6 

20 

20.  O 

.  o 

80 

79-9 

4.2 

40 

139.8 

7-3 

200 

199.  7 

10^5 

60 

259-6 

13.6 

21 

21.  O 

.  I 

81 

80.9 

4.2 

141 

140.  8 

7-4 

2CI 

200.  7 

10.5 

261 

260.  6 

13-7 

22 

22.0 

.  2 

82 

81.9 

4-3 

42 

141.8 

7-4 

O2 

201.  7 

io.  6 

62 

261.6 

I3.7 

23 

23.  o 

.2 

83 

82.9 

4-3 

43 

142.8 

7-5 

°3 

202.  7 

io.  6 

63 

262.  6 

13-8 

24 

24.  o 

•  3 

84 

83-9 

4.4 

44 

143-8 

7-5 

04 

203.7 

10.7 

64 

263.6 

13-8 

25 

25.0 

•  3 

85 

84.9 

4.4 

45 

144.8 

7-6 

05 

204.  7 

10.7 

65 

264.  6 

«3-9 

26 

26.0 

•4 

86 

85-9 

4-5- 

46 

145.8 

7-6 

06 

205.7 

10.8 

66 

265.6 

>3-9 

27 

27.0 

•  4 

87 

86.9 

4.6 

47 

146.8 

7-7 

07 

206.  7 

10.8 

67 

266.6 

14.  o 

28 

28.0 

•  5 

88 

87.9 

4.6 

48 

147.8 

7-7 

08 

207.7 

io.  9 

68 

267.6 

14.0 

29 

29.  o 

•  5 

89 

88.  9 

4-7 

49 

148.8 

7-8 

09 

208.  7 

io.  9 

69 

268.6 

14.1 

3° 

30.  o 

.6 

90 

89.  o 

4-7 

5° 

149.8 

7-9 

10 

209.7 

II.  0 

7° 

269.6 

14.1 

31 

31.0 

.6 

9' 

90.9 

4.8 

151 

150.8 

7-9 

211 

210.  7 

II.  0 

271 

270.  6 

14.2 

32 

32.0 

•  7 

92 

91.9 

4.8 

52 

151.8 

8.0 

12 

211.  7 

11.  i 

72 

271.  6 

14.2 

33 

33-0 

•  7 

93 

92.9 

4-9 

53 

152.8 

8.0 

13 

212.7 

n.  i- 

73 

272.  6 

14-3 

34 

34-o 

.8 

94 

93-9 

4-9 

54 

153-8 

8.  i 

'4 

213.7 

II.  2 

74 

273.6 

I4.3 

35 

35-  ° 

.8 

95 

94-9 

5-° 

55 

154.8 

8.1 

15 

214.7 

"•3 

75 

274.6 

14.4 

36 

36.  o 

•9 

96 

95-.  9 

5-° 

56 

155.8 

8.2 

16 

215.7 

"•3 

76 

275-6 

14.4 

37 

36-9 

•9 

97 

96.9 

57 

156.8 

8.2 

'7 

216.  7 

11.4 

77 

276.6 

14-5 

38 

37-9 

2.  O 

98 

97-9 

5-' 

58 

157.8 

8-3 

18 

217.7 

11.4 

78 

277-6 

14-5 

39 

38-9 

2.  O 

99 

98.9 

5-2 

59 

158.8 

8-3 

19 

218.  7 

11.5 

79 

278.6 

14.  6 

40 

39-9 

2.  I 

IOO 

99-9 

5-2 

60 

159.8 

8-4 

20 

219.7 

"•5 

So 

279.6 

14-7 

41 

40.9 

2.  I 

101 

100.9 

5-3 

161 

160.8 

8.4 

221 

220.  7 

II.  6 

281 

280.6 

14-7 

43 

41.9 

2.  2 

02 

101.  9 

5-3 

62 

161.8 

8-5 

22 

221.  7 

n.  6 

82 

281.6 

14.  $ 

43 

42.9 

2-3 

°3 

102.  9 

5-4 

63 

162.3 

8-5 

23 

222.  7 

11.7 

83 

282.6 

14.8 

44 

43-9 

2-3 

04 

163-9 

5-4 

64 

163.8 

8.6 

24 

223.7 

II.  7 

84 

283.6 

14.9 

45 

44-9 

2-4 

104.9 

5-5 

65 

164.8 

8.6 

25 

224.7 

ii.  8 

85 

284.6 

14.9 

46 

45-9 

2.4 

06 

i°5-9 

5-5 

66 

165.8 

8.7 

26 

225.7 

n.8 

86 

285.6 

15.0 

47 

46.9 

2-5 

°7 

106.  9 

5-6 

67 

166.8 

8-  7 

27 

226.  7 

11.9 

87 

286.6 

15.0 

48 

47-9 

2-5 

08 

107.9 

5-7 

63 

167.8 

8.8 

28 

227.7 

11.9 

88 

287.6 

15.1 

49 

48.9 

2.6 

09 

1  08.  9 

5-7 

69 

168.  8 

8.8 

29 

228.  7 

12.0 

89 

288.6 

15.1 

5° 

49-9 

2.6 

IO 

109.  8 

5-8 

70 

169.8 

8.9 

3° 

227.7 

12.  O 

90 

289.6 

15-2 

5' 

50.9 

•f.  7 

III 

i  io.  8 

5-8 

171 

170.8 

8-9 

231 

2:2.7 

12.  1 

291 

290.  6 

15.2 

52 

51.9 

2-7 

12 

in.  8 

5-9 

72 

171.8 

9.0 

32 

231.7 

12.  I 

92 

291.  6 

>5-3 

53 

52.9 

2.8 

13 

112.8 

5-9 

73 

172.8 

9-  i 

33 

232-  7 

12.2 

93 

292.  6 

>5-3 

54 

53-9 

2.8 

14 

113.8 

6.0 

74 

173-8 

9-1 

34 

233-  7. 

12.  2 

94 

293.6 

'5-4 

55 

54-9 

2.9 

15 

114.8 

6.0 

75 

174.8 

9-2 

35 

234-  7 

'2-3 

95 

294.6 

»5-4 

56 

55-9 

2.9 

16 

115.8 

6.1 

76 

175-8 

9-2 

36 

235-7 

I2.4 

96 

295.6 

'5-5 

57 

56.9 

3-0 

17 

116.8 

6.1 

77 

176.8 

9-3 

37 

236.  7 

12.4 

97 

296.  6 

15-5 

58 

57-9 

3-° 

18 

117.8 

6.2 

78 

177-8 

9-3 

38 

237-7 

I2.5 

98 

207.  6 

15.  6 

'59 

58.9 

3-1 

19 

118.8 

6.2 

79 

178.8 

9-4 

39 

238.7 

12.  5 

99 

298.6 

15.6 

60 

59-9 

.  3-  ' 

20 

•119.8 

6-3 

86 

179.8 

9-4 

.  40 

239-7 

12.  6 

300 

299.6 

'5-7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

[For  87  Degrees. 

116 


DIFFERENCE  OF  LATITUDE 

AND  DEPARTURE  FOR  4°. 

Dist 

Lat. 

Dep. 

bist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

I 

I.O 

0.  I 

61 

60.  9 

4-3 

121 

120.  7 

8-4 

181 

180.6 

12.6 

24' 

240.4 

16.  8 

2 

2.  O 

0.  I 

62 

61.8 

4-3 

22 

121.  7 

8-5 

82 

181.6 

12.7 

42 

241.4 

16.  9 

3 

3-  ° 

0.  2 

63 

62.8 

4-4 

23 

122.7 

8.6 

83 

182.6 

12.8 

43 

242.4 

17.0 

4 

4.0 

o.  3 

64 

63.8 

4-5 

24 

123.7 

8.6 

84 

183.6 

12.8 

44 

243-4 

17.0 

5-° 

o.  3 

65 

64.8 

4-5 

25 

124.7 

8-7 

85 

184-5 

12.9 

45 

244.4 

17.1 

6 

6.0 

o-4 

66 

65.8 

4.6 

26 

125.7 

8.8 

86 

'85.5 

13.0 

46 

245-4 

17.2 

7 

7.0 

(j-j 

66.8 

4-  7 

27 

126.  7 

8.9 

87 

186.5 

13.0 

47 

246.4 

17-2 

8 

8.0 

o!6 

68 

67.8 

4-7 

28 

127.7 

8.9 

88 

187.5 

13.1 

48 

247-4 

17.3 

9 

9.0 

0.6 

69 

68.8 

4-8 

29 

128.  7 

9.0 

89 

188.5 

13.2 

49 

248.4 

17.4 

10 

10.  O 

°-  7 

70 

69.8 

4-9 

3° 

129.7 

9-1 

90 

189.5 

'3-3 

50 

249.4 

17.4 

ii 

11.  0 

0.8 

71 

70.8 

5-  ° 

131 

13°.  7 

9.1 

191 

190.5 

'3-3 

25' 

250.4 

17-5 

12 

12.  O 

0.8 

72 

71.8 

5-o 

32 

'3'-7 

9.2 

92 

191.5 

'3-4 

52 

251.4 

17.6 

13 

13-0 

0.9 

73 

72.8 

33 

132.7 

9-3 

93 

192.  5 

'3-5 

53 

252.4 

17.6 

H 

14.0 

.  o 

74 

73-8 

5-2 

34 

133-7 

9-3 

94 

193-5 

'3-5 

54 

253-4 

17-7 

15 
IO 

I|.0 

16.  o 

.  o 
.  I 

9 

74-8 
75-  8^ 

5-2 

5-3 

a 

134-7 
135-7 

9-4 
9-5 

96- 

194-5 
195-5 

13-  6 
13-7 

H 

254.4 
255-4 

'7-8 
'7-9 

17 

17.0 

.2 

77 

76.8 

5-4 

37 

136.7 

9-6 

97 

'3-7 

57 

256.4 

'7-9 

18 

18.  o 

•  3 

78 

77.8 

5-4 

38 

137-7 

9.6 

98 

'97-5 

'3-8 

38 

257-4 

18.  o 

'9 

19.  o 

•  3 

79 

78.8 

5-5 

39 

138.7 

9-7 

99 

198.5 

'3-9 

59 

258.4 

18.  i 

20 

20.  O 

•4 

80 

79-8 

5-6 

40 

139-  7 

9-8 

200 

199-5 

14.  o 

60 

259-4 

18.  i 

21 

20.  9 

•  5 

Si 

80.8 

5-7 

141 

140.7 

9-8 

ZOI 

200.  5 

14.  o 

261 

260.4 

18.  2 

22 

21.  9 

•  5 

82 

81.8 

5-7 

42 

141.7 

9-9 

02 

201.5 

14.  i 

62 

261.4 

18.3 

23 

22.9 

.6 

83 

82.8 

5-8 

43 

142.7 

IO.  O 

°3 

202.  5 

14.2 

63 

262.4 

'8-3 

24 

23.9 

•  7 

84 

83.8 

5-9 

44 

143.6 

IO.  O 

04 

203.5 

14.2 

64 

263.4 

18.4 

25 

24.9 

•  7 

85 

84.8 

5-9 

45 

144.6 

IO.  I 

°5 

204.5 

'4-3 

65 

264.4 

18.5 

26 

25.9 

.8 

86 

85.8 

6.0 

46 

145-6 

IO.  2 

06 

205.5 

14.4 

66 

265.4 

18.6 

27 

26.  9 

9 

87 

86.8 

6.  i 

47 

1^6.6 

10.3 

07 

206.  5 

14.4 

67 

266.3 

18.6 

28 

27.9 

2.  O 

88 

87.8 

6.1 

48 

147.6 

IO.  3 

08 

207.5 

14.5 

68 

267.3 

18.7 

29 

28.9 

2.0 

89 

SS.  8 

6.2 

49 

148.6 

lo.  4 

09 

208.5 

14.  6 

69 

268.3 

18.  8 

3° 

29.9 

2.  I 

90 

89.8 

6-3 

50 

149.6 

10.5 

IO 

209.  5 

14.  6 

70 

269.3 

18.8 

3i 

3°-9 

2.  2 

9' 

90.8 

6-3 

'51 

150.0 

10.  5 

211 

2IO-.  5 

14-7 

271 

270.3 

18.9 

32 

3'-9 

2.  2 

92 

91.8 

6.4 

52 

151.  6 

10.  6 

12 

211.  5 

14.8 

72 

27'-  3 

19.  o 

33 

32.9 

2-3 

93 

92.8 

6-5 

53 

152.  6 

10.7 

13 

212.5 

14  9 

73 

272.3 

19.0 

34 

33-9 

2.4 

94 

93-8 

6.6 

54 

'53-6 

10.  7 

H 

213.5 

14.9 

74 

273-3 

19.1 

35 

34-9 

2.4 

95 

94-8 

6.6 

55 

154-6 

10.8 

15 

214.5 

15.0 

75 

274-3 

19.2 

36 

35-9 

2.5 

96 

95-8 

6.7 

56 

155.6 

10.  9 

16 

215.5 

IS-' 

76 

275-3 

19-3 

37 

f. 

36-9 

2.6 

97 

96.8 

6.8 

57 

156.6 

I  I/O 

17 

216.5 

15.1 

77 

276.3 

19-3 

38 

37-9 

2.-7 

98 

97-8 

6.8 

58 

157.6 

II.  0 

18 

217.5 

15.2 

78 

277-3 

19-4 

39 

38.9 

2.7 

99 

98.8 

6.9 

59 

158.6 

II.  I 

'9 

218.5 

15-3 

79 

278.3 

19-5 

40 

39-9 

2.8 

100 

99-8 

7.0 

60 

159.6 

II.  2 

20 

219.5 

'5-3 

80 

279-3 

19-5 

41 

40.9 

2.9 

IOI 

100.  8 

7.0 

161 

160.6 

II.  2 

221 

220.  5 

15.4 

281 

280.3 

19.6 

42 

41.9 

2.9 

02 

101.  8 

62 

161.6 

11-3 

22 

221-5 

15-5 

82 

281.3 

19.7 

43 

42.9 

3-o 

03 

102.  7 

7-2 

63 

162.6 

II.4 

23 

222.  5 

15-6 

83 

282.3 

19-7 

44 

43-9 

3-1 

04 

103-7 

7-3 

64 

163.6 

II.4 

24 

223.5 

15.6 

84 

283-3 

19.8 

45 

44-9 

05 

104.  7 

7-3 

65 

164.  6 

ii.  5 

25 

224-5 

15-7 

!l 

284.3 

19.9 

46 

45-9 

3-2 

06 

105.7 

7-4 

66 

165.6 

ii.  6 

26 

225.4 

15-8 

86 

285.3 

20.0 

47 

46.9 

3-3 

07 

106.  7 

7-5 

67 

166.6 

ii.  6 

27 

226.4 

15.8 

I7 

286.3 

20.0 

48 

47-9 

3-3 

08 

107.  6 

7-5 

68 

167.6 

11-7 

28 

227.4 

I5.9 

88 

287.3 

20.  I 

49 

48.9 

3-4 

09 

1  08.  7 

7.6 

69 

168.6 

n.  8 

29 

228.4 

16.  o 

89 

288.3 

2O.  2 

5° 

49-9 

3-5 

IO 

109.7 

7-7 

70 

169.  6 

11.9 

3° 

229.4 

16.  o 

90 

289.3 

20.2 

5' 

5°-9 

3-6 

III 

no.  7 

7-7 

I7i 

170.  6 

II-9 

23' 

230.4 

16.  i. 

291 

290.3 

20.3 

5L9 

3-6 

12 

111.7 

7-8 

72 

171.6 

12.0 

32 

231.4 

16.  2 

92 

291.3 

2O.4 

53 

52.9 

3-7 

13 

112.  7 

7-9 

73 

172.6 

12,  I 

33 

232.4 

16.3 

93 

292.3 

20.4 

54 

53-9 

3-8 

14 

113.7 

8.0 

74 

173-6 

12.  I 

34 

233-  4 

16.3 

94 

293-3 

20.5 

55 

54-9 

3-8 

'5 

114.7 

8.0 

75 

174-6 

12.2 

35 

234.4 

16.4 

95 

294-3 

20.  6 

56 

55-9 

3-9 

16 

115.7 

8.1 

76 

175-6 

12.3 

36 

235-4 

16.5 

96 

295-3 

20.  6 

57 

56-9 

4.0 

17 

116.7 

8.2 

77 

176.6 

12-3 

37 

2.36.4 

16.5 

97 

296.3 

20.  7 

58 

57-9 

4.0 

18 

117.7 

8.2 

78 

177.6 

12.4 

38 

237-4 

16.  6 

98 

297.3 

20.8 

59 

58.9 

4-1 

•?9 

118.  7 

8.3 

79 

178.6 

12-5 

39 

238.4 

16.7 

99 

298.3 

20.9 

60 

59-9 

4.2 

20 

119-7 

8.4 

80 

17976 

12.6 

40 

239-4 

16.7 

300 

299-3 

20.  9 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

[For  86  Degrees. 

117 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  5°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.  O 

0.  I 

61 

60.8 

5-3 

121 

1  20.  5 

10.5 

181 

180.3 

IS.8 

24I 

240. 

21.  0 

2 

2.  O 

0.2 

62 

61.8 

5-4 

22 

121.  5 

10.  6 

82 

181.3 

15-9 

42 

24I. 

21.  1 

3 

3-° 

°.  3 

63 

62.8 

5.5 

23 

122.5 

10.7 

83 

182.3 

«5-9 

43 

242. 

21.2 

4 

4.0 

o-3 

64 

63.8 

5-6 

24 

123-5 

10.8 

84 

183-3 

16.  o 

44 

243- 

21.3 

5.  o 

0.4 

65 

64.8 

5-7 

124.5 

10.  9 

85 

184.3 

16.  i 

45 

244. 

21.4 

7 

6.  o 

7.0 

o.  6 

66 

67 

a? 

5-8 
5-8 

27 

125-5 
126.  5 

II.  0 

n.  i 

86 
87 

&.J 

16.2 
16.3 

47 

245- 
246. 

21.4 
21.5 

8 

8.0 

0.7 

68 

67-7 

5-9 

28 

127.5 

II.  2 

88 

187.3 

16.4 

48 

247- 

21.6 

9 

y.  o 

0.8 

69 

03.7 

6.0 

29 

128.5 

II.  2 

89 

188.3 

16.5 

49 

248. 

21.7 

IO 

10.  O 

0.9 

70 

69.7 

6.  i 

30 

129.5 

"•3 

90 

189.3 

16.6 

5° 

249.0 

21.8 

n 

II.  O 

.  0 

71 

70.  7 

6.2 

131 

130.5 

II.4 

191 

190.3 

16.  6 

251 

250.  o 

21.9 

12 

12.  O 

.0 

72 

71-7 

6-3 

32 

131.  5 

ii.  s 

92 

I9"1-  3 

16.  7 

52 

251.0 

22.  O 

13 

13.0 

.  i 

73 

72.7 

6.4 

33 

132.5 

n.  6 

93 

192.3 

16.  8 

53 

252.0 

22.  J 

'4 

13-9 

.  2 

74 

73-7 

6-4 

34 

133-  5 

"•7 

94 

'93-3 

16.  9 

54 

253.0 

22.  I 

'5 

14.9 

•3 

75 

74-7 

6.5 

35 

'34-5 

ii.  8 

95 

194-3 

17.0 

55 

254.0 

22.2 

16 

15.9 

•4 

76 

75-7 

6.6 

36 

«3S-5 

11.9 

96 

'95-3 

17.1 

56 

255-0 

22.  3 

17 

16.9 

.  5 

77 

76.7 

6-7 

37 

'36-S 

11.9 

97 

196.3 

17.2 

57 

256.0 

22.  4 

18 

17-9 

.  6 

78 

77-7 

6.8 

38 

«37-S 

12.  O 

98 

197.2 

«7-3 

58 

257.0 

22.5 

19 

18.9 

•  7 

7Q 

78.7 

6.9 

39 

'38-5 

12.  I 

99 

198.2 

'7-3 

59 

258.0 

22.  6 

20 

19.9 

•  7 

80 

79,7 

7.0 

40 

'39-5 

12.  2 

200 

199.2 

17.4 

60 

259.0 

22.7 

21 

20.  9 

.8 

81 

80.  7 

7-  ' 

141 

140.5 

12-3 

201 

200.  2 

17-5 

261 

260.  o 

22.  7 

22 

21.9 

•9 

82 

81.7 

7-  * 

42 

141-5 

I2.4 

O2 

201.2 

17.6 

62 

261.  o 

22.8 

23 

22.9 

2.  O 

83 

82.7 

7-2 

43 

142-5 

12.5 

°3 

2O2.  2 

17-7 

63 

262.  o 

22.9 

2-1 

23-9 

2.  I 

84 

83.7 

7-3 

44 

'43-5 

12.6 

04 

203.  2 

17.8 

64 

263.  o 

23.0 

25 

24.9 

2.2 

85 

84-7 

7-4 

45 

144.4 

12.6 

05 

204.2 

17.9 

65 

264.  o 

23.1 

|P 

zo 

25.9 

2-3 

86 

85.7 

7-5 

46 

145-4 

12.7 

OO 

-205.  2 

18.  o 

66 

265.  o 

23-2 

27 

26.9 

2-4 

87 

86.  7 

7.6 

47 

146.4 

12.8 

07 

2OO.  2 

18.0 

67 

266.  o 

23-3 

23 

27.9 

2.4 

8S 

87.7 

7-7 

48 

147.4 

12.9 

08 

207.  2 

18.  i 

68 

267.0 

23-4 

29 

28.9 

2.5 

89 

88.  7 

7-8 

49 

148.4 

13.0 

09 

208.2 

18.2 

69 

268.0 

23.4 

3° 

29.9 

2.6 

90 

89.7 

7.8 

5° 

149.4 

I3-I 

IO 

209.  2 

iS-3 

70 

269.  o 

23-5 

31 

30.9 

2.7 

9' 

90.7 

7-9 

151 

150.4 

"3-2 

211 

210.  2 

18.4 

271 

270.  o 

23.6 

•33 

3'-9 

2.8 

92 

91.6 

8.0 

52 

151.4 

13-2 

12 

211.  2 

18.5 

72 

271.  o 

23.7 

33 

32-9 

2.9 

93 

92.  6 

8.1 

53 

152.4 

13.  3 

13 

212.2 

18,6 

73 

272.0 

23-8 

34 

33-9 

3-0 

94 

93-6 

8.2 

54 

153-4 

»3-4 

14 

213.2 

18.7 

74 

273.0 

23-9 

35 

34-9 

3-1 

95 

94-6 

8-3 

55 

154.4 

13-5 

15 

214.2 

18.7 

75 

274.0 

24.0 

35-9 

3-  i 

96 

95-6 

8.4 

56 

155-4 

13-6 

16 

215.2 

18.8 

76 

274.9 

24.1 

37 

36.9 

3-2 

97 

96.  6 

8-5 

57 

156.4 

13-7 

17 

2l6.  2 

18.9 

77 

275-9 

24.  I 

38 

37-9 

3-3 

98 

97-6 

8-5 

58 

157-4 

13-8 

18 

217.2 

19.0 

78 

276.9 

24,2 

39 

3-4 

99 

98.6 

8.6 

59 

158.4 

'3-9 

19 

218.2 

19.1 

79 

277-9 

24-3 

40 

•59.8 

3-5 

100 

99.6 

8.7 

60 

'59-  4 

J3-9 

20 

219.  2 

19.2 

So 

278.9 

24-4 

41 

40.8 

3-6 

101 

100.  6 

£.8 

161 

160.4 

14.  o 

221 

22O.  2 

19-3 

281 

279.9 

24.5 

42 

41.8 

3-7 

02 

101.6 

8.9 

62 

161.4 

14.1 

22 

221.2 

19-3 

82 

280.  9 

24.6 

43 

42.8 

3-7 

°3 

102.  C 

9.0 

63 

162.4 

14.2 

23 

222.2 

19.4 

83 

281.9 

24.  7 

44 

43-8 

3-8 

04 

103.  6 

9.1 

64 

163.4 

14-3 

24 

223. 

19-5 

84 

282.9 

24.8 

45 

44.8 

3-9 

°5 

104.  6 

9-2 

65 

164.4 

14.4 

25 

224. 

19.  6 

85 

283.9 

24.8 

46 

45-8 

4.0 

oo 

105.  6 

9-2 

66 

165.4 

14-  5 

26 

225. 

I9.7 

86 

284.9 

24.9 

47 

46.8 

4-1 

07 

1  06.  6 

9-3 

67 

166.4 

14.6 

27 

226. 

19.8 

ll 

285.9 

25.0 

48 
49 

47-8 
48.8 

4.2 
4-3 

08 

09 

107.6 

108.6 

9-4 
9-5 

68 
69 

167.4 
168.4 

14.6 
14.7 

28 

29 

227. 
228. 

19.9 
20.  o 

88 
89 

286.9 

287.9 

25.1 
25.2 

49.8 

4-4 

IO 

109.6 

9.6 

70 

169.4 

14.8 

30 

229. 

20.  o 

9° 

288,9 

25-3 

Si 

50.8 

4-4 

111 

no.  6 

9-7 

171 

170.3 

14.9 

231 

230. 

20.  i 

291 

289.9 

25.4 

52 

51.3 

4-5 

12 

in.  6 

9-8 

72 

I7I.3 

15.0 

32 

23L 

2O.  2 

92 

290.9 

25-4 

S3 

52.8 

4.6 

13 

112.  6 

9.8 

73 

172.3 

15.  I 

33 

232. 

20.3 

93 

291.9 

25-  5 

54 

53-8 

4'  7 

H 

113.6 

9-9 

74 

173-3 

15-2 

34 

233- 

2O.4 

94 

202.  9 

25.6 

55 

S-t-3 

4.8 

IS 

114.6 

10.  O 

75 

174-3 

>5-3 

35 

234- 

20.  5 

95 

293-9 

25.  7 

56 
17 

55.8 

55.3 

4-9 

16 
17 

115.6 
116.6 

10.  I 

10.2 

70 

n 

175.3 
176.3 

iS-3 
15.4 

36 

235- 

20.  6 
20.7 

97 

294.9 
295.9 

25.8 
25.9 

58 

57-8 

j.  i 

18 

117.6 

10.3 

7* 

177-3 

15-5 

3» 

237. 

20.7 

9« 

296.9 

26.0 

59 

58.8 

5-  ' 

19 

118.5 

10.4 

178.3 

15.6 

39 

238. 

20..8 

99 

297-9 

26.  i 

60 

59.8 

5-2 

20 

>i9-5 

10.5 

& 

179-3 

15-7 

40 

239. 

20.  9 

300 

298.9 

26.  i 

Dbt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lit. 

Dist. 

Dep. 

Lat. 

[For  85  Degrees. 

110 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  G°. 

Ulst. 

Lit. 

Dep. 

Dlst 

LaL 

Dep. 

DIsL 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

DisL 

LaL 

Dep. 

I 

I.  O 

O.  I 

61 

60.  7 

6.4 

121 

120.3 

12.6 

181 

180.0 

18.9 

241 

239-7 

25.2 

2 

2.  0 

o.  2 

62 

61.7 

6-5 

22 

121.3 

12.8 

82 

181.0 

19.  o 

42 

240.  7 

25-3 

3 

3.0 

o-3 

63 

62.7 

6.8 

•    23 

122.3 

12.9 

83 

182.0 

19.  I 

43 

241.7 

25-4 

4 

4-0 

0.4 

64 

63.6 

6.7 

24 

'23.3 

13-0 

84 

183.  o 

19.2 

44 

242.  7 

25-5 

I 

7 

fr° 

6.0 
7.0 

o.  5 
o.  6 
o-  7 

3 

67 

64.6 
65.6 
66.6 

6.8 
6.9 
7.0 

11 
27 

124.  3 

125.3 
126.  3 

I3-I 
13-2 
13-3 

85 
86 

S7 

184.0 
185.0 
1  86.  0 

19-3 
19.4 

'9-5 

45 
46 

47 

243-  7 
244.  7 
245.6 

25.6 

25-7 
25.8 

8 

8.0 

o.S 

68 

67.6 

7-  i 

28 

127-3 

I3.4 

88 

187.0 

19-7 

4» 

246.  6 

25.9 

9 

9.0 

0.9 

bg 

68.0 

7-2 

29 

128.3 

13-5 

89 

iSS.  o 

19.  8 

49 

247.6 

26.  o 

10 

9-9 

I.  0 

7° 

69.6 

7-3 

3° 

129-3 

13-6 

90 

189.  o 

19.9 

5° 

248.6 

26.  1 

II 

10.  9 

.  I 

7" 

70.  6 

7-4 

131 

i30-3 

13-7 

191 

190.  o 

20.  o 

251 

249.6 

26.  2 

12 

11.9 

•  3 

72 

71.6 

7-5 

32 

I3I.3 

13-8 

92 

190.9 

20.  I 

52 

250.  6 

26.3 

13 

12.9 

•  4 

73 

72.6 

7.6 

33 

132-3 

13-9 

93 

191.9 

20.  2 

53 

251.  6 

26.  4 

14 

'3-9 

74 

73-6 

7-  7 

34 

I33.3 

14.  o 

94 

192.9 

20-3 

54 

252.  6 

26.6 

15 

14.9 

.  6 

75 

74.6 

7-8 

35 

134-3 

14.  1 

95 

193-9 

20.  4 

55 

253-6 

26.7 

16 

'5-9 

•  7 

T6 

75-6 

7-9 

36 

135-3 

14.2 

96 

194.9 

20.5 

56 

254-6 

26.8 

17 

16.  9 

.8 

77 

76.6 

8.  o 

37 

136.2 

14.3 

97 

195-9 

20.  6 

57 

255-6 

26.  9 

18 

'7-9 

•  9 

73 

77-6 

8.2 

3« 

137-2 

14.4 

98 

196.9 

20.7 

58 

256.  6 

27.0 

19 

18.9 

2.  0 

79 

78.6 

8-3 

39 

138.2 

14.  5 

99 

197.9 

20.8 

59 

257.6 

27.1 

20 

19.  9 

2.  I 

So 

79-6 

8.4 

40 

139-2 

14.6 

200 

198.9 

20.  9 

60 

258.6 

27.2 

21 

20.  9 

2.  2 

Si 

80.6. 

8-5 

141 

140.  2 

14-  7 

201 

199.9 

21.  0 

261 

259.6 

27-3 

22 

21.9 

2-3 

82 

81.6 

8.6 

42 

141.  2 

14.8 

02 

200.  9 

21.  I 

62 

260.  6 

27.4 

23 

22.9 

2-4 

83 

82-5 

8.7 

43 

142.3 

14.9 

°3 

201.  9 

21.  2 

63 

261.6 

27-5 

24 

23-9 

2.  5 

84 

83.5 

8.8 

44 

143-2 

i5-i 

04 

202.  9 

21-3 

64 

262.6 

27.  6 

25 

24-9 

2.6 

85 

84.5 

8.9 

45 

144.2 

IS.  2 

°5 

203.9 

21.4 

65 

263-5 

27.7 

26 

25.9 

2-  7 

86 

85.5 

9.0 

46 

145.2 

I5.3 

06 

204.9 

21.  5 

66 

264.5 

27-8 

27 

26.9 

2.8 

87 

86.5 

9.1 

47 

146.  2 

15.4 

07 

205.9 

21.  6 

67 

265-5 

27.9 

28 

27.8 

2.9 

88 

87.5 

9-  2 

48 

147-2 

15-  5 

08 

206.  9 

21.7 

68 

266.  5 

28.0 

19 

28:8 

3-° 

89 

88.5 

9-3 

49 

148.2 

15.6 

09 

207.9 

21.8 

69 

267.5 

28.  i 

3° 

29.8 

3-i 

90 

89-5 

9-4 

5° 

149.2 

15.7 

10 

208.8 

22.  0 

70 

268.5 

28.2 

3! 

30.8 

3-2 

9" 

90.5 

9-5 

151 

150.  2 

15.8 

211 

209.8 

22.  I 

271 

269.5 

2*.  3 

32 

3>.8 

3-3 

92 

91-5 

9.6 

S2 

I5I.2 

15-9 

12 

210.8 

22.  2 

72 

270.5 

28.  4 

'   33 

32.8 

3-4 

93 

92.5 

9-  7 

53 

152.2 

16.  o 

13 

211.  8 

22.3 

73 

271.5 

28.5 

34 

33-8 

3-6 

94 

93-5 

9.8 

54 

153-2 

16.  I 

H 

212.8 

22.4 

74 

272.5 

28.  6 

35 

34-8 

3-7 

95 

94-5 

9-9 

55 

154-2 

16.  2 

15 

213.8 

22.5 

75 

273-5 

28.7 

36 

35-8 

3-8 

96 

95-5 

10.  O 

56 

155- 

16.3 

16 

214.8 

22.6 

76 

274.5 

28.8 

37 

36.8 

3-9 

97 

96.5 

10.  I 

57 

156. 

16.4 

17 

215.8 

22.7 

77 

275-5 

29.0 

3» 

37-8 

4.0 

98 

97-5 

10.2 

5« 

157- 

16.5 

18 

216.8 

22.8 

78 

276-5 

29.  I 

39 
40 

38.8 
39-8 

4-  I 
4-2 

99 

loo 

98.5 
99-5 

10-3 

10-5 

59 

60 

I5S. 

'59- 

16.  6 
16.7 

19 

20 

217.8 
218.8 

22.  9 

23.  o 

B 

277-5 
278.5 

29.  2 
29-3 

41 

40.5 

4-3 

101 

100.  4 

10.  6 

161 

1  60. 

16.8 

221 

219.8 

23-1 

281 

279-5 

20.  4 

42 

41.8 

4-4 

02 

101.  4 

10.7 

62 

161. 

16.  9 

22 

220.8 

23.2 

82 

28,0.5 

29-5 

43 

42.8 

4-5 

°3 

102.4 

10.  8 

63 

162. 

17.0 

23 

221.8 

23-3 

83 

281.4 

29.  6 

44 

43-8 

4-6 

04 

103-4 

10.9 

64 

163. 

17.  i 

24 

222.8 

23-4 

84 

282.4 

29-7 

45 

44-8 

4-7 

°5 

104,4 

II.  0 

65 

164. 

17.2 

25 

223.8 

23.5 

85 

283.4 

29.8 

46 

45-7 

4-8 

06 

105.4 

II.  I 

66 

165. 

17.4 

26 

224.8 

23.  6 

86 

284.4 

29.9 

47 

46.7 

4-9 

°7 

loo.  4 

II.  2 

6? 

1  66. 

17-5 

27 

225.  8 

23-7 

87 

285.4 

30.  o 

48 

47-7 

5-° 

08 

107.4 

II.3 

68 

167. 

17.6 

28 

226.8 

23-8 

88 

286.  4 

30.1 

49 

48.7 

5-  ' 

09 

108.4 

1  1.  4 

69 

1  68. 

17-7 

29 

227.7 

23-9 

89 

287.4 

30.2 

5° 

49-  7 

5-2 

10 

109  4 

11.5 

70 

169. 

17.8 

3° 

228.  7 

24.0 

90 

288.4 

3°-3 

5' 

5°-7 

5-3 

in 

110.4 

n.  6 

171 

170. 

17-9 

231 

229.  7 

24.1 

291 

289.4 

3°-4 

52 

5'-  7 

5-4 

12 

ill.  4 

ii.  7 

72 

171. 

18.  o 

S2 

230.7 

24-3 

92 

290.4 

30.5 

53 

52-7 

5-5 

13 

112.4 

n.  8 

73 

172. 

18.  i 

33 

231.7 

24-4 

93 

291.4 

30  6 

54 

53-7 

5-6 

14 

"3-4 

11.9 

74 

173-0 

l&.Z 

34 

232.7 

24-5 

94 

292.4 

30.  7 

55 

54-7 

5-7 

15 

"4-4 

12.  0 

75 

174.0 

18.3 

35 

233.7 

24.  6 

95 

293-4 

30.8 

56 

55-7 

5-9 

16 

115.4 

12.  I 

76 

175.0 

18.4 

3° 

234-  7 

24-7 

96 

294-4 

3°-9 

57 

56.7 

6.  o 

«7 

116.4 

12.  2 

77 

176.0 

18.5 

37 

235-7 

24-8 

97 

295-4 

31.0 

58 

57-7 

6.1 

iB 

117.4 

12-3 

78 

177.0 

18.  6 

38 

236.7 

24,9 

98 

296.4 

31-' 

g 

58.7 
59.7 

6.2 

6-3 

19 

20 

118.3 
>i9-3 

12.4 

12.5 

e 

178.0 
179.0 

IS.  7 

18,8 

39 
40 

237.7 
238.7 

25.0 
25.1 

99 
300 

297.4 
298.4 

3'-3 
3'-4 

DUt 

Dep. 

Lit. 

Dlit. 

Dep. 

Lit. 

Diet. 

Dep. 

Lac. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lit 

[For  84  Degrees. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  7°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

o.  I 

6l 

6o.S 

7-4 

121 

120. 

14-7 

181 

»79-  7 

22.  I 

241 

239-2 

29.4 

2 

2.  O 

0.  2 

62 

61.5 

7-6 

22 

121. 

14.9 

82 

180.6 

22.2 

42 

240.  2 

29.5 

3 

3-0 

0.4 

63 

62.5 

7-7 

23 

122. 

15.0 

83 

181.6 

22-3 

43 

241.  2 

29.  6 

4 

4.0 

0.5 

64 

63.5 

7-8 

24 

'23- 

I5.I 

84 

182.6 

22.4 

44 

242.  2 

29.7 

5 

5-  ° 

0.6 

65 

64.5 

7-9 

25 

124. 

15.2 

85 

183.6 

22.5 

45 

243-2 

29-9 

6 

6.0 

0-7 

66 

65-5 

8.0 

26 

125. 

15.4 

86 

184  6 

22.7 

46 

244.2 

30.0 

7 

6.9 

0.9 

67 

66.5 

8.2 

27 

126. 

'5-5 

87 

185.6 

22.8 

47 

245.  2 

30.1 

8 

7-9 

I.  0 

68 

67.5 

8-3 

28 

127.  o 

'5-6 

88 

186.  6 

22.9 

48 

246.2 

30.  2 

9 

8.9 

I.  I 

69 

68.5 

8.4 

29 

128.0 

'5-7 

89 

187.6 

23.0 

49 

247. 

3°-3 

10 

9-9 

I.  2 

70 

69.5 

8-5 

30 

129.  o 

15.8 

90 

188.6 

23.2 

So 

248. 

30-5 

ii 

10.  9 

'•3 

7' 

70.5 

8.7 

130.0 

16.  o 

191 

189.6 

23-3 

251 

249. 

30.6 

12 

11.9 

'•I 

72 

7'-5 

8.8 

32 

131.0 

16.  i 

92 

190.6 

23-4 

250. 

3°-7 

'3 

12.9 

1.6 

73 

72.5 

8.9 

33 

132.0 

16.  2 

93 

191.  6 

23-5 

53 

251. 

30.8 

'4 

'3-9 

'-7 

74 

73-4 

9.0 

34 

'33-o 

'6-3 

94 

192.  6 

23.6- 

54 

252. 

31.0 

'5 

14.9 

1.8 

75 

74-4 

9-' 

35 

'34-0 

16.5 

95 

'93-5 

23-8 

55 

253- 

16 

15.9 

1.9 

76 

75-4 

9-3 

36 

'35-o 

16.6 

96 

'94-5 

23-9 

56 

254. 

31.2 

'7 

16.9 

2.  I 

77 

76.4 

9-4 

37 

136.  o 

16.7 

97 

'95-5 

24.0 

57 

255- 

18 

'7-9 

2.2 

78 

77-4 

9-5 

38 

'37-0 

16.8 

98 

196.5 

24.  I 

58 

256. 

31-4 

'9 

18.9 

2-3 

79 

78.4 

9-6 

39 

138.0 

16.  9 

99 

'97-5 

24-3 

59 

257- 

3'-6 

20 

19.9 

2.4 

80 

79-4 

9-7 

40 

139.0 

17.  ' 

.  200 

198.5 

24.4 

60 

258.. 

3'-7 

21 

20.8 

2.6 

81 

80.  4 

9-9 

141 

'39-9 

17.2 

20  1 

>99-5 

24-5 

261 

259.1. 

3'-  8 

22 

21.8 

2-7 

82 

81.4 

10.  o 

42 

140.9 

'7-3 

02 

200.  5 

24.  6 

62 

26o.O 

3'-9 

23 

22.8 

2.8 

83 

82.4 

10.  I 

43 

141.9 

'7-4 

°3 

201.5 

24-7 

63 

26l.O 

32-1 

24 

23.8 

2.9 

84 

83.4 

10.2 

44 

142.9 

'7-5 

04 

202.  5 

24.9 

64 

262.O 

32-2 

25 

24.8 

3-° 

85 

84.4 

10.4 

45 

'43-9 

'7-7 

°5 

203.5 

25.0 

65 

263.0 

32.3 

26 

25.8 

3-2 

86 

85.4 

10.5 

46 

144.9 

'7-8 

06 

204.5 

25.1 

66 

264.  o 

32-4 

11 

26.8 
27.8 

3-3 
3-4 

87 
88 

86.4 
87-3 

10.  6 

47 
48 

'45-9 
146.9 

'7-9 
18.0 

2 

205.5 
206.  4 

25.2 
25-3 

67 
68 

265.0 

266.  o 

32.5 
32-7 

29 

28.8 

3-5 

89 

88.3 

10.8 

49 

'47-9 

18.  2 

09 

207.4 

25-5 

69 

267.0 

32-8 

3° 

29.8 

3-7 

90 

89.3 

II.  0 

5° 

148.9 

18.3 

10 

208.4 

25.6 

70 

268.0 

32-9 

3' 

30.8 

3-8 

9' 

90.3 

II.  i 

'5' 

149.9 

18.4 

211 

209.4 

25-7 

271 

269.0 

33-  ° 

31-8 

3-9 

92 

9'-  3 

II.  2 

52 

150.9 

18.5 

12 

210.  4 

25.8 

72 

27O.O 

33-1 

33 

32.8 

4.0 

93 

92-3 

"•3 

53 

151.9 

18.  6 

'3 

211.  4 

26.0 

73 

271.0 

33-3 

34 

33-7 

4.1 

94 

93-3 

11.5 

54 

152.9 

1  8.  8 

'4 

212.4 

26.1 

74 

272.O 

33-4 

35 

34-7 

4-3 

95 

94-3 

u.6 

55 

'53-8 

18.9 

15 

213-4 

26.2 

75 

273-0 

33-5 

36 

35-7 

4-4 

96 

95-3 

M.  7 

56 

'54-8 

19.  o 

1  6 

214.4 

26.  3 

I6 

273-9 

33-6 

37 

36.7 

4-5 

97 

II.  8 

57 

155.8 

19.' 

'7 

215.4 

26.4 

n 

274-9 

33-8 

38 

37-7 

4.6 

98 

97-3 

11.9 

58 

156.8 

'9-3 

18 

216.  4 

26.6 

78 

275-9 

33-9 

39 

38.7 

4.8 

99 

98-3 

12.  I 

59 

'57-8 

19.4 

'9 

217.4 

26.7 

79 

276.9 

34-.0 

40 

39-7 

4-9 

100 

99-3 

12.  2 

60 

158.8 

'9-5 

20 

218.4 

26.8 

80 

277.9 

34-1 

4' 

40.  7 

5-° 

IOI 

100.  2 

12-3 

161 

139-8 

19.  6 

221 

219.4 

26.  9 

281 

278.9 

34-2 

42 

41.7 

S-1 

02 

IOI.  2 

12.4 

62 

160.  8 

'9-7 

22 

220.  3 

27-1 

82 

279-9 

34-4 

43 

42.7 

5-2 

03 

102.2 

12.6 

63 

161.8 

19.9 

23 

221.  3 

27.2 

83 

280.9 

34-S 

44 

43-7 

5-4 

04 

103.  2 

'2-7 

64 

162.8 

20.  o 

-24 

222.3 

27-3 

84 

281.9 

34-0 

45 

44-  7 

5-5 

°5 

104.  2 

12.8 

65 

163.8 

20.  I 

25 

223.3 

27.4 

85 

282.9 

34-7 

46 

45-7 

5-6 

06 

105.  2 

12.9 

66 

164.8 

2O.  2 

26 

224.3 

27.5 

86 

283.9 

34-9 

47 

46.6 

5-7 

07 

1  06.  2 

13.0 

67 

165.8 

20.  4 

27 

225.3 

27-7 

87 

284.9 

35-° 

48 

47-6 

5-8 

08 

107.  2 

'3-2 

68 

166.7 

20.  5 

28 

226,  3 

27.8 

88 

285.9 

35-1 

49 
5° 

48.6 
49.6 

6.0 
6.1 

09 
10 

108.  2 
log.  2 

'3-3 
'3-4 

69 

70 

167.7 
168.7 

20.  6 
20.  7 

29 

30 

227.3 

228.3 

27.9 

28.0 

89 

90 

286.8 
287.8 

35-2 
35-3 

51 

50.6 

6.2 

III 

IIO.  2 

'3-5 

171 

169.7 

20.8 

23l 

229.3 

28.2 

291 

288.8 

35-5 

52 

51.6 

6-3 

12 

III.  2 

'3-6 

72 

170.7 

21.0 

32 

230.3 

28.3 

92 

289.8 

35-6 

53 

52.6 

6.5 

'3 

112.  2 

'3-8 

73 

171.7 

21.  I 

33 

23'-  3 

28.4 

93 

290.  S 

35-7 

54 

53-6 

6.6 

'4 

II3.2 

'3-9 

74 

172.7 

21.  2 

34 

232-3 

28.5 

94 

291.8 

35-8 

ii 

54-6 
55-6 

6.7 

6.  § 

II 

114. 
"5- 

14.0 
14.1 

H 

«73-7 
»74-7 

21.  A 

35 
36 

233-2 

234.2 

28.6 
28.8 

3 

292.8 
293.8 

36.0 
36.J 

57 

56.6 

6.9 

'7 

116. 

'4-3 

n 

'75-  7 

21.6 

3Z 

235.2 

28.9 

n 

294-3 

36-* 

58 

8 

57-6 
58.6 
59-6 

7.2 
7-3 

18 
'9 

20 

117. 

118. 
119. 

14.4 
14.  S 
14.6 

76 
11 

176.7 

177.7 
178.7 

"•I 
21.8 

21.9 

38 

39 
40 

236.2 
237.2 
238.2 

29.O 
29.  I 
29.2 

98 

99 

300 

295-8 
296.8 

297-8 

ft! 

DM. 

Dep. 

Ut. 

Dlit. 

Dep. 

Ut. 

Dirt. 

Dtp. 

Lit. 

Dist. 

Dep. 

Lat. 

Dfct, 

Dep. 

Ut 

[For  83  Decrees. 

120 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  8°. 

Dlst. 

Lat. 

Dep. 

Disl. 

Lat 

Dep. 

Oist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dlst. 

Lai 

Dep. 

I 

I.  O 

0.  I 

61 

60.  4 

8-5 

121 

119.8 

1  6.  8 

iSl 

179.2 

25.2 

241 

2j8.7 

33-5 

2 

2.  O 

o.  3 

62 

61.4 

8.6 

22 

120.8 

17.0 

82 

180.  2 

25-3 

42 

239.6 

33-7 

3 

3-  ° 

o.  4 

63 

62.4 

8.8 

23 

121.  8 

I7.I 

83 

181.2 

25-5 

43 

240.  6 

33-8 

4 

4.0 

0.6 

64 

63.4 

8.9 

24 

122.8 

'7-3 

84 

182.  2 

25.6 

44 

241.  6 

34-0 

1 

5-° 
5-9 

0.7 
0.8 

a 

64.4 
65.4 

9.0 
9.2 

11 

123.  8 

124.8 

17.4 
'7-5 

§ 

183.  2 
184.  2 

25-7 
25.9 

45 
46 

242.  6 
243-6 

34-' 
34-2 

7 

6.9 

.  o 

67 

66.3 

9-3 

2? 

125.8 

'7-7 

87 

185.2 

26.  o 

47 

244-  6 

34-4 

8 

7.9 

.  i 

68 

67.3 

9-  5 

28 

126.8 

17.8 

88 

186.  2 

26.2 

48 

245.6 

34-5 

9 

8.9 

.  3 

69 

68.3 

9-6 

29 

127.7 

18.  o 

89 

187.2 

26.  3 

49 

246.  6 

34-7 

10 

9-9 

•  4 

7° 

69-  3 

9-7 

3° 

128.  7 

1  8.  i 

90 

188.2 

26.  4 

5° 

247.6 

34-8 

II 

10.  9 

•  5 

7' 

7°-3 

9-9 

'3' 

129.7 

1  8.  2 

191 

I89. 

26.6 

251 

248.  6 

34-9 

12 

n.  9 

•  7 

72 

71-3 

10.  O 

32 

'3°-  7 

>8.  4 

92 

190. 

26.7 

52 

249-  5 

35-i 

'3 

12.9 

.8 

73 

72.3 

IO.  2 

33 

'3'-7 

18.5 

93 

191. 

26.  9 

53 

250.5 

35-2 

H 

•3-9 

•  9 

74 

73-3 

10-3 

34 

132-7 

18.  6 

94 

192. 

27.0 

54 

25'-5 

35-3 

15 

14.9 

2.  I 

75 

74-3 

10.  4 

35 

133-7 

18.  8 

95 

193- 

27.1 

55 

252.5 

35-5 

16 

15.8 

2.  2 

76 

75-3 

lo.  6 

36 

«34-  7 

18.9 

96 

194. 

27-3 

56 

253-5 

35-6 

17 

16.  8 

2-4 

77 

76-3 

10.  7 

37 

'35-7 

19.  i 

97 

195- 

27.4 

57 

254-5 

35-8 

18 

17.8 

2-  5 

78 

77-2 

10  9 

38 

'36.7 

19.  2 

98 

196. 

27.6 

58 

255-5 

35-9 

'9 

18.  8 

2.6 

79 

78.2 

II    0 

39 

'37-7 

'9-3 

99 

197. 

27-7 

59 

256-5 

36.  o 

20 

19.8 

2.8 

So 

79.2 

u   i 

40 

138.6 

'9-5 

200 

19*. 

27.8 

60 

257-5 

36.2 

21 

20.? 

2.9 

Si 

80.2 

"•3 

'4' 

'39-6 

19.  6 

2O  I 

199.0 

28.0 

261 

258-5 

36-3 

22 

21.8 

3-  ' 

82 

Si.  2 

11.4 

42 

140.  6 

19.8 

02 

2OO.  O 

28.1 

62 

259-5 

36.5 

23 

22.8 

3.2 

83 

82.2 

n.  6 

43 

141.6 

19.9 

°3 

2OI.  O 

28.3 

°3 

260.  4 

36  6 

24 

23.8 

3-3 

84 

83.2 

II.  7 

44 

142.6 

20.  o 

04 

202.  0 

28.4 

64 

261.  4 

.A  7 

11 

24.8 

25-  7 

3-5 
3-6 

85 
86 

84.2 
85.2 

n.  8 

12.0 

45 
46 

'43-  6 
144.6 

20.  2 
20.3 

°5 
06 

203.  o 
204.  o 

28.5 
28.7 

11 

262.  4 
263.4 

36-9 
37-0 

27 

26.  7 

3-8 

87 

86.2 

12.  I 

47 

145.6 

20.5 

07 

205.  o 

28.  8 

67 

264.4 

37-2 

28 

27.  7 

3-9 

88 

87. 

12.  2 

48 

146.  6 

20.  6 

08 

206.  o 

28.9 

68 

265.4 

37-3 

29 

28.7 

4.0 

89 

88. 

12.4 

49 

'47-  5 

20.  7 

09 

207.  o 

29.  i 

69 

266.  4 

37-4 

3° 

29.  7 

4-2 

90 

89. 

12.5 

5° 

148.5 

20.  9 

10 

208.  o 

29.  2 

7° 

267.4 

37-6 

3' 

30.  7 

4-3 

9' 

90. 

12.7 

'5' 

'49-5 

21.  O 

211 

208.  9 

29.4 

271 

268.  4 

37-7 

32 

3'-  7 

4-5 

92 

9'- 

12    8 

52 

ISO'S 

21.  2 

12 

209.9 

29.5 

73 

269.4 

37  9 

33 

32.  7 

4-6 

93 

92. 

12.9 

53 

151.5 

21-3 

'3 

210.9 

29.  6 

73 

270.3 

7?..  0 

34 

33-7 

4-7 

94 

93- 

'3-' 

54 

152.5 

21.4 

'4 

211.  9 

29.8 

74 

27'-  3 

38.1 

35 

34-7 

4-9 

95 

94- 

'3-2 

55 

'53-5 

21.  6 

15 

212.  9 

29.9 

75 

272.3 

38-3 

36 
37 

35-6 
36.6 

5.0 

5-  ' 

96 
97 

s 

'3-4 
'3-5 

56 
57 

'54-5 
'55-5 

21.7 
21.9 

'7 

2'3-9 
214.9 

30.1 
30.2 

76 
77 

273-3 
2/4-3 

38.4 
38.6 

38 

37-6 

5-3 

98 

97.0 

'3-6 

58 

156.5 

22.  0 

18 

215.  9 

3°-3 

78 

275-3 

38.7 

39 

38.6 

5-4 

99 

98.0 

'3-8 

59 

'57-5 

22.  I 

'9 

210.  9 

3°-5 

79 

2/6-3 

38.8 

40 

39-  6 

S.6 

100 

99.0 

'3-9 

60 

158.4 

22.3 

20 

217.9 

30.  6 

80 

2-7-3 

39-0 

4' 

40.  6 

5-7 

101 

loo.  o 

14.1 

161 

159.4 

22.4 

221 

218.8 

30.8 

281 

278-3 

39-1 

42 

41.6 

5-8 

02 

IOI.O 

14.2 

62 

1  60.  4 

22-5 

22 

219.8 

3°-9 

82 

279-3 

39-2 

43 

42.6 

6.0 

°3 

IO2.  O 

'4-3 

63 

161.  4 

22.7 

23 

220.8 

31.0 

83 

280.  2 

39-4 

44 

43-6 

6.1 

04 

103.0 

14-5 

64 

162.  4 

22.8 

24 

221.  8 

31.2 

84 

28l.  2 

39-5 

45 

44.6 

6-3 

°5 

104.  o 

14.  6 

65 

163-4 

23.0 

25 

222.8 

3'-3 

85 

282.2 

39-7 

46 

45.6 

6-4 

06 

105.  o 

14.8 

66 

164.4 

23.1 

26 

223.8 

3'-  5 

86 

283.  2 

39-8 

47 

46.5 

6-5 

07 

IOD.O 

14.9 

67 

165.4 

23.2 

27 

224.8 

3'.6 

87 

284.2 

39-9 

48 

47-5 

6.7 

08 

106.  9 

15.0 

68 

1  66.  4 

23.4 

28 

225.  8 

3'-  7 

88 

285.  2 

40.  i 

49 

48.5 

6.8 

09 

107.9 

15.2 

69 

167.  4 

23-5 

29 

226.8 

3'-9 

89 

2S6.2 

40.2 

5° 

49-5 

7.0 

10 

1  08.  9 

'5-3 

70 

168.3 

23-7 

3° 

227.8 

32.0 

90 

287.  2 

40.4 

5' 

5°-5 

7-1 

III 

109.9 

15-4 

'7' 

'69.3 

23.  8 

23' 

228.8 

32.1 

291 

288.  2 

40.5 

52 

5'-5 

7-2 

12 

110.9 

'5-6 

72 

I70-3 

23-9 

S2 

229.7 

32-3 

92 

289.  2 

40.  6 

53 

52-5 

7-4 

'3 

111.9 

'5-7 

73 

I7I-3 

24.1 

33 

230.7 

32-4 

93 

290. 

40.  8 

54 

53-5 

7-5 

H 

112.  J 

15-9 

74 

"72.3 

24.2 

34 

231.7 

32.6 

94 

291. 

40-9 

55 

54-5 

I'l 

15 

113-9 

IO.  O 

75 

'73-3 

24.4 

35 

232.7 

32.7 

95 

292. 

41.  « 

5& 

55-5 

7-8 

16 

II4.9 

16.  I 

76 

174-3 

24.5 

36 

233-7 

32.8 

96 

293- 

41.2 

$ 

& 

56.4 

57-4 
58.4 
59-4 

7-9 
8.1 

8.2 

8-4 

11 

'9 
20 

II5.9 

116,  o 
117.8 
118.8 

16.3 
l6.,i 
16.6 
16.7 

9 
& 

175.3 
176.3 
177-3 
170.2 

<M.  6 

24.8 
24.9 
25.1 

37 
38 

39 

40 

234-7 

235-  7 
236-7 
237-7 

33-0 
33-' 
33-3 
33-4 

97 
98 

99 
300 

294. 

295- 
296. 

297- 

4'-3 
41.5 
41.  6 
41.8 

Dlst. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat 

Dlst. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

[For  82  Degrees. 

121 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  9°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dcp. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0.2 

6t 

60.  2 

9-5 

121 

119.5 

18.9 

181 

178.8 

28.3 

241 

236.0 

37-7 

2 

2.0 

°.-3 

62 

61.2 

9-7 

22 

120.  5 

I9.I 

82 

179-8 

28.5 

42 

239.0 

37-9 

3 

3-° 

o.  5 

63 

62.2 

9-9 

23 

121.  5 

19.2 

83 

180.  7 

28.6 

43 

240.0 

38.0 

4 

4.0 

o.  6 

64 

63.2 

IO.  O 

24 

122.5 

19.4 

84 

181.7 

zB.S 

44 

241.0 

38.2 

4-9 

0.8 

65 

64.  2 

IO.  2 

25 

I23-5 

19,.  6 

85 

182.  7 

28.9 

45 

242.  o 

38.3 

6 

5-9 

0.9 

66 

65.2 

10.3 

26 

124.4 

19.7 

86 

183-7 

29.1 

46 

243.0 

38.5 

7 

6.9 

1.  1 

67 

66.2 

10.5 

27 

125.4 

19.9 

87 

184.7 

29-3 

47 

244.0 

38.6 

8 

7-9 

'•3 

68 

67.2 

10.6 

28 

126.4 

20.  o 

88 

185.7 

29.4 

48 

244,9 

38.8 

9 

8.9 

1.4 

69 

68.2 

10.8 

29 

127.4 

2O.  2 

89 

186.7 

29.  6 

49 

245.9 

39-0 

10 

9-9 

1.6 

•jo 

69.  i 

II.  0 

3" 

128.4 

20.3 

90 

187-7 

29.7 

5° 

246.9 

39-  1 

ii 

10.9 

'•7 

7" 

70. 

u.  i 

'31 

129.4 

20.  5 

191 

188.6 

29-9 

251 

247.9 

39-3 

12 

11.9 

1.9 

72 

7'. 

"•3 

32 

130.4 

20.  6 

92 

189.6 

30.  o 

S2 

248.9 

39  4 

'3 

12.8 

2.  O 

73 

72. 

11.4 

33 

>3'-4 

20.8 

93 

190.6 

30.2 

53 

249-9 

39-0 

'4 

13-8 

2.  2 

74 

73- 

n.  6 

34 

132.4 

21.  O 

94 

191.6 

3°-3 

54 

250.9 

39-7 

15 

14.8 

2-3 

75 

74- 

11.7 

35 

"33-  3 

21.  I 

95 

192.  6 

30-5 

55 

251.9 

39-9 

16 

15.8 

2-5 

76 

75- 

11.9 

36 

'34-3 

21-3 

96 

193.6 

3°-7 

56 

252.8 

40.0 

'7 

16.  8 

2.7 

77 

76. 

12.  O 

37 

'35-3 

21.4 

97 

194.6 

30.8 

57 

253-8 

4O.  2 

18 

17.8 

2.8 

78 

77.0 

12.2 

38 

136-3 

21.  6 

98 

195.6 

31.0 

58 

254.8 

40.4 

>9 

18.  8 

3-° 

79 

78.0 

I2.4 

39 

137-3 

21.  7 

99 

196.5 

31-1 

59 

255-8 

40.5 

20 

19.8 

3-  ' 

80 

79.0 

'2-5 

40 

138-3 

21.9 

200 

197-5 

31-3 

60 

256.8 

40.7 

21 

20.  7 

3-3 

Ti 

80.0 

12.7 

141 

'39-3 

22.  I 

20  1 

198.5 

3'-4 

261 

257-8 

40.8 

22 

21.7 

3-4 

82 

Si.o 

12.8 

42 

140.3 

22.  2 

02 

199-5 

31-6 

62 

258.8 

41.0 

23 

22.  7 

3-6 

83 

82.0 

13.0 

43 

141.  2 

22.4 

°3 

200.  5 

31-8 

63 

259.8 

41.1 

24 

23-7 

3-8 

84 

83.0 

'3-' 

44 

142.  2 

22.5 

04 

201.5 

31-9 

64 

260.  7 

41.3 

25 

24.7 

3-9 

85 

84.0 

'3-3 

45 

143.2 

22.7 

°5 

202.  5 

32.1 

65 

261.  7 

41.5 

26 

25-7 

4.1 

86 

84.9 

13-5 

46 

144.2 

22.8 

06 

2°3-5 

32.2 

66 

262.  7 

41.6 

27 

26.7 

4-2 

87 

85.9 

13-6 

47 

J45-2 

23.0 

07 

204.5 

32-4 

6l 

263.7 

41.8 

28 

27.7 

4-4 

88 

86.9 

13-8 

48 

146.2 

23.2 

08 

205.4 

32.5 

68 

264.7 

41.9 

29 

28.6 

4-5 

89 

87-9 

'3-9 

49 

147.2 

23-3 

09 

206.  4 

32-7 

69 

265.7 

42.1 

3° 

29.6 

4-7 

90 

88.9 

14.1 

5° 

148.2 

23-5 

10 

207.4 

32.9 

70 

266.7 

42.2 

3! 

30.6 

4.8 

9' 

89.9 

14.2 

151 

149. 

23-6 

211 

208.  4 

33-0 

271 

267.  7 

42.4 

32 

3i.6 

5.0 

92 

90.9 

14.4 

S2 

150. 

23-8 

12 

209.4 

33-2 

72 

268.7 

42.6 

33 

32.6 

5-2 

93 

91.9 

14.5 

53 

151. 

23-9 

'3 

210.4 

33-3 

73 

269.  6 

42.7 

34 

33-6 

5-3 

94 

92.8 

14.7 

54 

152. 

24.1 

14 

211.4 

33-5 

74 

270.6 

42.9 

35 

34-6 

5-5 

95 

93-8 

14.9 

55 

'53- 

24.2 

15- 

212.4 

33-6 

75 

271.6 

43-o 

36 

35-6 

5-6 

90 

94.8 

15.0 

56 

154. 

24-4 

16 

213-3 

33-8 

76 

272.6 

43-2 

37 

36.5 

5-8 

97 

95-8 

15.2 

57 

155-- 

24.  6 

17 

214-3 

33.9 

77 

273.6 

43-3 

38 

37-5 

5-9 

98 

96.8 

'5-3 

58 

156. 

24.7 

18 

215-3 

34-1 

7» 

274.6 

43-5 

39 

38.5 

6.1 

99 

97.8 

•5-5 

59 

157.0 

24.9 

J9 

216.  3 

34-3 

79 

275.6 

43-6 

40 

39-5 

6-3 

IOO 

98.8 

IS.  6 

60 

158.0 

25.0 

20 

217-3 

34-4 

80 

276.6 

43-8 

4' 

40.5 

6.4 

101 

99-8 

15.8 

161 

159.0 

25.  2 

221 

218.3 

34-6 

281 

.277-  5 

44-0 

42 

41.5 

6.6 

02 

:oo.  7 

16.  o 

62 

160.0 

25.3 

22 

2  '9-  3 

34-7 

82 

278.5 

44'-  I 

43 

42.5 

6-7 

°3 

101.  7 

16.  i 

63 

161.0 

25-5 

23 

220.3 

34-9 

83 

279.5 

44-3 

44 

43-5 

6.9 

04 

102.  7 

16.3 

64 

162.6 

25-7 

24 

221.2 

35-0 

84 

280.5 

44-4 

45 

44-4 

7.0 

°5 

103.7 

16.4 

65 

163.0 

25.8 

25 

222,2 

35-2 

fi 

281.5 

44:6 

46 

45-4 

7-2 

06 

104.7 

16.6 

66 

164.  o 

26.0 

26 

223.  2 

35-4 

86 

282.5 

44-7 

47 

46.4 

7-4 

07 

105.  7 

16.  7 

67 

564.9 

26.1 

27 

224.2 

35-5 

87 

283:5 

44-9 

48 

47-4 

7-5 

08 

106.  7 

16.9 

68 

165.9 

26.3 

28 

225.2 

35-7 

OQ 
00 

284.5 

45.1 

49 

48.4 

7-7 

09 

107.7 

17-1 

69 

166.9 

26.4 

29 

226.  2 

35-8 

89 

285.4 

45-2 

5° 

49-4 

7-8 

10 

108.  6 

17.2 

70 

167.9 

26.6 

10 

227.2 

36.0 

90 

286.4 

45-4 

5' 

50.4 

S.o 

III 

109.  6 

17-4 

171 

168.9 

26.8 

231 

228.2 

3f.i 

291 

287.4 

45-5 

S2 

51.4 

8.1 

12 

uo.  6 

'7-5 

72 

169.9 

26.9 

32 

229. 

36.3 

92 

288.4 

45-7 

53 

52-3 

8-3 

*3 

in.  6 

17.7 

73 

170.9 

27.1 

33 

230. 

36.4 

93 

289.4 

45.  8 

54 

53-3 

8.4 

«4 

112.  6 

17.  8 

74 

171.9 

27.2 

34 

231. 

36.6 

94 

290.4 

46.0 

55 

54-3 

8.6 

15 

113.6 

18,0 

75 

172.8 

27.4 

35 

232. 

36.8 

95 

291.4 

46.  i 

56 

53-3 

8.8 

16 

114.6 

i3.  i 

76 

173-8 

27-5 

36 

233- 

36-9 

96 

292.4 

46.3 

57 

56-3 

8.0 

»7 

115.  6 

18.3 

77 

174.8 

27-  7 

37 

234- 

37-1 

97 

293-3 

46.5 

5» 

57-3 

9.1 

18 

116.  5 

18.5 

78 

175-8 

27.8 

38 

235- 

37-2 

68 

294-3 

46.  6 

59 

58.3 

9-2 

19 

117.5 

18.6 

79 

576.8 

28.0 

39 

236. 

37-4 

99 

295-3 

46.  8 

60 

59-3 

9-4 

20 

118.5 

18.8 

So 

s  7,7-8 

40 

237.0 

37-5 

300 

296.3 

46.9 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  81  Degrees. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  10°. 

Dlst. 

Lai. 

Dcp. 

Dist. 

Lat. 

Dcp. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dcp. 

Dlst. 

Lai. 

Dcp. 

I 

1.0 

0.2 

61 

60.  I 

10.  6 

121 

119.  2 

21.  0 

181 

>7S-3 

3'-4 

241 

237-  3 

41.8 

2 

2.  O 

o.  3 

62 

61.  I 

10.8 

22 

120. 

21.  2 

82 

179.2 

31.6 

42 

.  -3s-  3 

42.0 

3 

3-° 

0.5 

63 

62.  o 

10.  9 

23 

121. 

21.4 

83 

I  So.  2 

3'-8 

43 

239-  3 

42.2 

4 

3-9 

o.  7 

64 

63.  o 

11.  I 

24 

122. 

21.5 

84 

181.  2 

32.0 

44 

240-3 

42.4 

5 

4-9 

0.9 

65 

64.  o 

"•3 

25 

I23- 

21.7 

85 

182.2 

32-1 

45 

24I-3 

42.5 

6 

5-9 

.0 

66 

65.  o 

11.5 

20 

124. 

21.9 

86 

183.2 

32-3 

46 

242-3 

42.7 

7 

6.9 

.  2 

67 

66.0 

n.  6 

27 

125. 

22.  I 

8/ 

184.  2 

32-5 

47 

243-2 

42.9 

8 

7-9 

•  4 

68 

67.0 

11.  8 

28 

126. 

22.  2 

8S 

I85. 

32.0 

48 

244.2 

43-  « 

9 

8.9 

.6 

69. 

68.0 

12.  O 

29 

127.  o 

22.4 

89 

1  86. 

32-8 

49 

245.2 

43-2 

10 

9.8 

•  7 

70 

68.9 

12.  2 

3° 

128.0 

22.  6 

90 

187. 

33-  ° 

5° 

246.  2 

43-4 

II 

10.8 

'•9 

7' 

69.9 

I2-  3 

'3' 

129.  o 

22.7 

191 

1  88. 

33-  2 

251 

247.2 

43-  6 

12 

n.  8 

2.  I 

72 

70.9 

12.5 

32 

130.  o 

22.  9 

92 

189- 

33-3 

52 

248.  2 

43-8 

>3 

12.8 

2.3 

73 

71.9 

12.7 

33 

131.0 

23-' 

93 

190. 

33-5 

53 

249.2 

43-9 

14 

'3-8 

2.4 

74 

72.9 

12.8 

34 

132.  o 

23-3 

94 

191. 

33-7 

54 

250. 

44.  i 

15 

14.8 

2.6 

75 

73-9 

'3-° 

35 

132.9 

23-4 

95 

192.  o 

33-9 

55 

251. 

44-3 

ID 

15.8 

2.8 

76 

74-8 

«3-2 

36 

«33-9 

23.6 

96 

'93-° 

34-0 

56 

252. 

44-5 

17 

16.7 

3-° 

77 

75-8 

13.4 

37 

'34-9 

23-8 

97 

194.0 

34-2 

57 

253- 

44.6 

18 
19 

'7-7 
18.7 

3-1 
3-3 

78 
79 

76.8 
77-8 

'3-5 
'3-7 

3» 
39 

'35-9 
i36-9 

24.0 
24.  i 

98 
99 

195.0 
196.  o 

34-4 

34-6 

58 
I9 

254. 

252' 

44-8 
45.0 

20 

«9-7 

3-5 

So 

78.8 

«3-9 

40 

137-9 

24-3 

200 

197.0 

34.7 

60 

256. 

45-' 

21 

20.  7 

3-6 

81 

79.8 

14.  i 

141 

'38.9 

24.5 

20  1 

197-9 

34-9 

261 

257.0 

45-3 

22 

21.  7 

3-8 

82 

80.8 

14.2 

42 

139-8 

24.7 

02 

198.9 

35-' 

62 

258.0 

45-5, 

23 

22.  7 

4.0 

83 

81.7 

14.4 

43 

140.  8 

24.8 

°3 

199.9 

35-3 

63 

259.0 

45-7 

24 

23.6 

4-  2 

84 

82.7 

14.  6 

44 

141.8 

25.0 

04 

200.  9 

35-4 

64 

260.  o 

45-8 

25 

"     ., 

24.  6 

4-3 

85 

83.7 

14.8 

45 

142.8 

25.2 

°5 

201.  9 

35-6 

^ 

261.  o 

46.  o 

26 

25.  6 

4-5 

86 

84-7 

14.9 

46 

143.8 

25-4 

06 

202.  9 

35-8 

66 

262.  o 

46.  2 

27 
28 

26.6 
27.  6 

4-7 
4-9 

87 
88 

86!  7 

15.1 

'5-3 

47' 
48 

144.8 
145-8 

25-4 
25.7 

07 
oS 

203.  9 

204.  tf 

3>9 
36.1 

67 
6S 

262.  9 
263.9 

46.4 
46.5 

2.9 

28.6 

5-° 

89 

87.6 

'5-5 

49 

146.7 

25.9 

09 

205.8 

36.3 

69 

264.9 

46.  7 

^0 

29.5 

5-2 

9° 

88.6 

iS-6 

5° 

147-7 

26.  o 

10 

206.  8 

36.5 

70 

265.9. 

46.9 

31 

3°-5 

5-4 

9' 

89.6 

15.8 

•5' 

148.7 

.~6.  2 

211 

207.  8 

36.  6 

271 

266.  9 

47.  i 

32 

3>-5 

5-6 

92 

90.  6 

16.  o 

52 

149.  7 

26.  4 

12 

208.8 

36.8 

72 

267.9 

47.2 

33 

32-5 

5-7 

93 

91.6 

16.  i 

53 

150.7 

26.6 

«3 

209.8 

37-0 

73 

268.9 

47-4 

34 

33-  5 

5-9 

94 

92.  6 

16.3 

54 

151.7 

26.7 

14 

210.  7 

37-2 

74 

269.8 

47-6 

35 

34-5 

6.  i 

95 

93-6 

16.5 

55 

152.  6 

26.9 

'5 

211.  7 

37-3 

75 

270.  8 

47.8 

36 

35.5 

6.3 

96 

94-5 

16.7 

56 

153-  6 

27.1 

16 

212.  7 

37-5 

70 

271.8 

47-9 

37 

36-4 

6.4 

97 

95-5 

16.  8 

57 

154.6 

27-3 

'7 

213-7 

37-7 

77 

272.8 

48.1 

38 

37-4 

•6.6 

98 

96.5 

17.0 

58 

155.6 

27.4 

18 

214.  7 

37-9 

78 

273-8 

4S.3 

39 
40 

38-4 
39-4 

6.8 
6.9 

99 

IOO 

97-5 
98.5 

17.2 
17.4 

g 

156.6 
157.6 

27.  6 
27-8 

19 

20 

215.  7 
216.  7 

38.0 
38-2 

79 
80 

274.8 
275-7 

4S.4 
48.6 

41 

40.4 

7-  ' 

101 

99-5 

'7-5 

161 

158.6 

28.0 

221 

217.6 

38.4 

281 

270.7 

48.8 

42 

41.4 

7-3 

02 

loo.  5 

17.7 

62 

>59-  5 

28.1 

22 

218.6 

3S.5 

82 

277.7 

49.0 

43 

42/3 

7-5 

°3 

foi.4 

17-9 

63 

1  60.  5 

28.3 

23 

219.  6 

38.7 

f3 

278.7 

49-  ' 

44 

43-3 

7-6 

04 

1  02.  4 

18.  i 

64 

161.  5 

28.5 

24 

220.  6 

38.9 

84 

279.7 

49-3 

45 

44-  3 

7.8 

05 

i°3-4 

18.2 

65 

162.  5 

28.7 

25 

221.  6 

39-  i 

85 

280.  7 

49-5 

46 

45-3 

8.0 

06 

104.4 

18.4 

66 

'63-5 

28.8 

26 

222.  6 

39-2 

86 

281.  7 

49-  7 

47 

46-  3 

8.2 

°7 

105.4 

18.  6 

67 

164.5 

29.  o 

27 

223.  6 

39-4 

87 

282.6 

49-8 

48 

47-3 

8-3 

08 

1  06.  4 

18.  8 

68 

165.  4 

29.  2 

2S 

224.5 

39-6 

SS 

283.  6 

50.0 

49 

48-3 

8-5 

09 

'°7-3 

18.9 

69 

1  66.  4 

29-3 

29 

225-5 

39-8 

89 

284.  6 

56.  2 

5° 

49-  2 

8.7 

10 

108.  i 

19.  i 

7° 

167.4 

29.5 

3° 

226.  5 

39-9 

9° 

285.  6 

50.4 

5' 

50.  2 

8-9 

in 

109.3 

19-3 

>7> 

168.4 

29.7 

23» 

227.5 

40.  i 

291 

286.  6 

5°-5 

52 

51.2 

9.0 

12 

no.  3 

19.4 

72 

169.4 

29.9 

32 

228.5 

4°-3 

92 

'287.6 

50.7 

53 

52.2 

9.2 

>3 

in.  3 

19.  6 

73 

170.4 

30.  o 

33 

229.5 

40.5 

93 

288.  5 

50.9 

54 

S3-2 

9-4 

14 

112.3 

19.8 

74 

171.4 

30.2 

34 

230.4 

40.  6 

94 

289.5 

5I.I 

55 

54.2 

9-6 

15 

"3-3 

20.  o 

75 

'72-3 

3°-4 

35 

231-4 

40.8 

95 

290.5 

51.2 

56 

55- 

9-7 

16 

114.  2 

20.  I 

76 

173-3 

30.  6 

36 

232.4 

41.0 

96 

291.5 

5I<1 

57 

56- 

9-9 

17 

115,2 

20.  3 

77 

174-3 

3°-7 

37 

233-4 

41.2 

97 

292.5 

51.  b 

58 

57- 

10.  I 

18 

1  1  6.  2 

20.  5 

7» 

175-3 

3°-9 

38 

234-4 

4'-  3 

98 

293-5 

S'-7 

59 

58. 

10.2 

19 

117.2 

20.7 

79 

176.3 

31.1 

39 

235-4 

41.5 

99 

294-5 

5'-9 

So 

59- 

10.4 

20 

I  l8.  2 

20.8' 

So 

177-3 

3«-3 

40 

236.4 

41-7 

300 

295-4 

52.1 

Dlst. 

Dcp. 

Lat.' 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  So  Degrees. 

123 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  11°. 

Dist 

LaL 

Dcp. 

Dist. 

LaL 

Dep. 

Dist. 

LaL 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.  0 

O.  2 

6l 

59-9 

II.  6 

i2I 

IlS.  8 

23.1 

181 

>77-  7 

34-5 

241 

236.  6 

46.  O 

2 

2.  0 

0.4 

62 

60.  9 

II   8 

22 

119.8 

23-3 

82 

178.7 

34-7 

42 

237-6 

46.  2 

3 

2.9 

0.6 

63 

61.8 

12.  O 

23 

120.  7 

23-5 

83 

179.6 

34-9 

43 

238-5 

46.4 

4 

3-9 

0.8 

64 

62.8 

12.2 

24 

121.  7 

23-7 

84 

180.  6 

35-  ' 

44 

239-  5 

46.6 

5 

4-9 

.0 

65 

63.8 

*2.'4 

25 

122.7 

23-9 

85 

181.6 

35-3 

45 

240.5 

46.7 

6 

5-9 

.  I 

66 

64.8 

12.6 

26 

123-7 

24.  o 

86 

182.6 

35-5 

46 

241.5 

46.9 

7 

6.9 

•3 

"7 

65.8 

12.8 

27 

124.  7 

24.2 

87 

183.6 

35-7 

47 

242.  5 

47-  I 

8 

7-9 

•  5 

t>8 

66.8 

13.0 

28 

125.  6 

24.4 

88 

184-5 

35-9 

48 

243-4 

47-3 

9 

8.8 

•  7 

09 

67.7 

'3-2 

29 

126.6 

24.  6 

89 

185-5 

3b.  i 

49 

244-4 

47-5 

10 

9-8 

•  9 

70 

68.  7 

13.4 

3° 

127.  6 

24.8 

90 

186.5 

36.  3 

50 

245.4 

47-7 

II 

10.  8 

2.  I 

71 

69.  7 

'3-5 

131 

•  128.  6 

25.0 

191 

187,5 

36-4. 

251 

246.4 

47-9 

12 

ii.  8 

2-3 

72 

70.7 

>3-  7 

32 

129.  6 

25.2 

92 

188.5 

36.6 

52 

247.4 

48.  i 

'3 

12.8 

2-5 

73 

71.  7 

13-9 

33 

130.  6 

25-4 

93 

189.5 

36.8 

53 

248.4 

48.3 

14 

13-7 

2.7 

74 

72.6 

14.1 

34 

I3I-5 

25.6 

94 

190.4 

37-0 

54 

249-3 

48.5 

'5 

14.7 

2.9 

75 

73-6 

14-3 

35 

132-5 

25.8 

95 

191.4 

37-2 

55 

250.3 

48.7 

16 

'5-7 

3-1 

76 

74-6 

M.5 

36 

133.5 

26.  o 

96 

192.4 

37-4 

56 

251-3 

48.8 

17 

16.7 

3-2 

77 

75-6 

14  7 

37 

'34-5 

26.1 

97 

193-4 

37-6 

57 

252.3 

49.0 

18 

17-7 

3-4 

78 

76.6 

14.9 

38 

135-5 

26.3 

98 

194-4 

37-8 

58 

253-3 

49-2 

19 

18.7 

3-6 

79 

77-5 

15.  i 

39 

136.4 

26.5 

99 

195-3 

38.0 

59 

.254.2 

49-4 

20 

19.  6 

3-8 

80 

78-5 

15-3 

40 

137-4 

26.7 

200 

196-3 

38.2 

60 

255.2 

49-6 

21 

20.  6 

4.0 

Si 

79-5 

15-5 

141 

138-4 

26.  9 

201 

"97-3 

38-4 

261 

256.  2 

49-8 

22 

21.6 

4-2 

82 

80.  5 

15.6 

42 

«39-4 

27.  i 

O2 

198.3 

38.5 

62 

257-2 

50.  o 

23 

22.  6 

4-4 

83 

81.5 

15.8 

43 

140.4 

27-3 

°3 

199.3 

38.7 

63 

258.2 

50.2 

24 

23-6 

4-6 

84 

82.5 

16.  o 

44 

141.4 

27-5 

04 

200.  3 

38.9 

64 

259. 

50.4 

25 

24-5 

4.8 

85 

83-4 

16.2 

45 

142-3 

27-7 

05 

201.  2 

39-1 

65 

260. 

50.  6 

26 

25-5 

5-° 

86 

84.4 

16.  4 

46 

'43-3 

27.9 

06 

202.  2 

39-3 

66 

26l. 

50.8 

27 

26.  5 

5-2 

87 

85.4 

16.  6 

47 

144-3 

28.0 

°7 

203.2 

39-5 

67 

262. 

50.9 

23 

27-5 

5-3 

88 

86.4 

16.  8 

48 

145-3 

28.2 

08 

204.  2 

39-7 

68 

263. 

51.1 

29 

28-5 

5-5 

89 

87.4 

17.0 

49 

146-3 

28.4 

09 

205.  2 

39-9 

69 

264. 

51-3 

3° 

29.4 

5-7 

99 

88.3 

17.2 

5° 

147.2 

28.6 

10 

206.  I 

40.  i 

70 

265.0 

51-5 

3' 

3°-4 

5-9 

9i 

89-3 

17.4 

15" 

148.  2 

28.8 

211 

207.  I 

4°-3 

271 

266.  o 

51-7 

32 

3'-4 

6.  i 

92 

9°-3 

17.6 

52 

149-2 

29.  o 

12 

208.  I 

40.5 

72 

267.0 

5<-9 

33 

32-4 

6-3 

93 

91-3 

«7-7 

53 

150.  2 

29.  2 

13 

209.  I 

40.  6 

73 

268.0 

52.1 

34 

33-4 

6.5 

94 

92-3 

17-9 

54 

I5I.2 

29.4 

14 

2IO.  I 

40.8 

74 

269.  o 

52.3 

35 

34-4 

6-7 

95 

93-3 

18.  i 

55 

152.  2 

29.  6 

15 

211.  0 

41.0 

75 

269.9 

52.5 

36 

35-3 

6.9 

96 

94.  2 

18.3 

56 

I53-I 

29.8 

16 

212.  O 

41.2 

76 

270.9 

52.7 

37 

36.3 

7-  i 

97 

95-2 

18.5 

57 

154.  I 

3°.  ° 

17 

213.0 

41.4 

77 

271.9 

52.9 

3« 

37-3 

7-3 

98 

96.  2 

18.7 

58 

155-1 

30.1 

18 

214.  o 

41.  6 

78 

272.9 

53-0 

39 

38.3 

7-4 

99 

97-2 

18.9 

59 

156.  I 

30.3 

19 

215.  o 

41.8 

79 

273.9 

53-2 

4° 

39-3 

7.6 

loo 

98.  2 

19.  i 

60 

I57.I 

30.5 

20 

216.  o 

42.0 

80 

274.9 

53-4 

41 

40.  2 

7.8 

101 

99- 

19-3 

161 

158.0 

3°-7 

221 

2  1  6.  9 

42.2 

281 

275.8 

53-6 

42 

41.2 

8.0 

02 

100. 

"9-5 

62 

159-0 

3°-9 

22 

217.9 

42.4 

82 

276.8 

53-8 

43 

42.2 

8.2 

°3 

101. 

19-  7 

63 

:6o.  o 

3I-1 

23 

218.9 

42.6 

83 

277.8 

54.0 

44 

43-2 

8.4 

04 

102. 

19.8 

64 

161.  o 

3"-3 

24 

219-9 

42.7 

84 

278.8 

54-2 

45 

44-2 

8.6 

°5 

1°3- 

20.  o 

65 

162.  o 

3'-5 

25 

220.  9 

42.9 

85 

279.8 

54-4 

46 

45-2 

8.8 

06 

I04. 

2O.  2 

66 

163.  o 

3i.7 

26 

221.8 

43-  ' 

86 

280.  7 

54-6 

47 

46. 

9-o 

07 

105.  o 

20.  4 

67 

>63-9 

3i-9 

27 

222.8 

43-3 

87 

281.  7 

54-8 

48 

47- 

9.  .2 

08 

1  06.  O 

20.  6 

68 

164.9 

32-1 

28 

223.8 

43-5 

88 

282.  7. 

55.0 

49 

4S. 

9-3 

09 

107.  o 

20.  S 

69 

165.9 

32.2 

29 

224.  8 

43-7 

89 

283.7 

55-1 

5° 

49- 

9-5 

10 

1  08.  O 

21.  0 

70 

1  66.  9 

32-4 

3° 

225.8 

43  9 

go 

284^7 

55-3 

51 

5°- 

9-7 

III 

109.  o 

21.  2 

171 

167.9 

32.6 

231 

22678 

44.  i 

291 

285-7 

55-5 

S2 

51.0 

9-9 

12 

109.9 

21.4 

72 

16?.  8 

32.8 

32 

227.7 

44-  3 

92 

286.6 

55-7 

53 

52.0 

10.  I 

'3 

1  10.  9 

21.6 

73 

169.8 

33-0 

33 

228.  7 

44-5 

93 

287.6 

55-9 

54 

53.0 

10.3 

14 

111.9 

21    8 

74 

170.8 

33-2 

34 

229.7 

44.6 

94 

288.6 

56.1    ' 

55 

54-0 

10.5 

15 

112  9 

21.9 

75 

171.8 

33-4 

35 

230.  7 

44-8 

95 

289.  6 

56.3 

56 

55-  ° 

10.7 

16 

113.9 

22.  I 

76 

172.8 

33-6 

36 

23>.7 

45-° 

96 

290.  6 

56.5 

57 

56.  o 

10.  9 

17 

114.  9 

22-3 

77 

«73-  7 

33-8 

37 

232.  6 

45-2 

97 

291.5 

56.7 

58 

S6  9 

ii.  i 

18 

115.8 

22.5 

73 

174-  7 

34-0 

38 

233.6 

45-4 

98 

292.5 

56.9 

59 

57-9 

"•3 

19 

116.8 

22.7 

79 

175-7 

34-2 

39 

234.6 

45-6 

99 

293-5 

57-i 

60 

58.9 

11.4 

20 

117.8 

22.9 

So 

170.  7 

34-3 

40 

235-6 

45-8 

300 

294-5 

57-2 

Dist. 

Dcp. 

Lat. 

DUt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist, 

Dcp. 

Lat. 

[For  79  Degrees. 

124: 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  12°. 

DUt. 

Lot. 

Dep 

Dlst. 

Ut 

Dep 

Utst 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

nist. 

Lit. 

Dep. 

i 

1.0 

O.  2 

61 

59-7 

'2.7 

121 

118.4 

25.2 

iSi 

177.0 

37-6 

241 

235-7 

50.  I 

3. 

2.0 

0.4 

62 

60.  6 

12.9 

22 

'19-3 

25-4 

82 

178.0 

37-8 

42 

236-7 

5°-3 

3 

2.9 

0.6 

63 

61.6 

13.' 

23 

120.  3 

25.6 

83 

1/9.0 

38.  o 

43 

237-7 

5°-5 

4 

3-9 

0.8 

64 

62.6 

•3-3 

24 

121.3 

25.8 

84 

180.  o 

38.3 

44 

238-7 

50.7 

5 

4-9 

1.0 

<>5 

63.6 

'3-5 

25 

122.3 

26.  o 

85 

181.0 

38.5 

45 

239.6 

50.9 

6 

5-9 

I.  2 

66 

64.6 

"3-7 

26 

123.2 

26.2 

86 

181.9 

38.7 

46 

240.  6 

51  « 

7 

6.8 

>-5 

67 

65.5 

'3-9 

27 

124.2 

26.4 

87 

182.9 

38.9 

47 

241.  6 

5'-4 

8 

7.8 

'•  7 

6S 

60.  5 

14.  i 

28 

125.2 

26.6 

88 

'83.9 

39-1 

48 

242.6 

51-6 

9 

8.8 

1.9 

69 

67.5 

14-3 

29 

126.  2 

26.8 

89 

184.9 

39-3 

49 

2*3-  6 

51.8 

10 

9.8 

2.  I 

70 

68.  5 

14.  6 

3° 

127.  2 

27.0 

90 

185.8 

39-5 

5° 

244-  5 

52.0 

ii 

10.  8 

2-3 

7i 

69.4 

14.8 

'31 

123.  I 

27.2 

191 

1  86.  8 

39-7 

251 

245-5 

52.2 

12 

11.7 

2-5 

72 

70.4 

15.0 

y- 

129.  I 

27.4 

92 

187.8 

39-9 

52 

246.5 

52.4 

'3 

12.7 

2.7 

73 

71.4 

15.2 

33 

130.  I 

27.7 

93 

1  88.  8 

40.  i 

53 

247-5 

52.6 

>4 

«3-7 

2.9 

74 

72.4 

15-4 

34 

i3«-  « 

27-9 

94 

189.8 

40.3 

54 

248.4 

52.8 

1C 

"4.  7 

3-i 

75 

73-4 

15.6 

35 

132.0 

28.  i 

95 

190.  7 

40.5 

55 

249.4 

53.0 

10 

'5-7 

3-3 

76 

74-3 

'5-8 

36 

'33-  ° 

28.3 

96 

191.7 

40.  8 

56 

250.4 

53-2 

'7 

16.6 

3-5 

77 

75-3 

16.  o 

37 

134-0 

28.5 

97 

192.  7 

41.0 

57 

251.4 

53-4 

Io 

17.6 

3-7 

78 

76.3 

1  6.  2 

38 

'35-o 

28.7 

98 

'93-7 

41.2 

58 

252.4 

53-6 

19 

18.  6 

4.0 

79 

77-3 

16.4 

39 

136.0 

28.9 

99 

194-7 

41-4 

59 

253-3 

53-8 

20 

19.  6 

4.2 

80 

78.3 

16.  6 

40 

'36.9 

20.  I 

200 

195.6 

41.  6 

60 

254-3 

54.1 

21 

20.5 

4-4 

Si 

79.2 

16.8 

141 

137.9 

29-3 

201 

196.6 

41.8 

261 

255.3 

54-3 

22 

21.5 

4.6 

82 

80.2 

17.0 

42 

138.9 

29.5 

O2 

197.6 

42.  o 

62 

256.3 

54-5 

23 

22.5 

4-8 

83 

81.2 

'7-3 

43 

>39-9 

29.7 

°3 

198.  6 

42.2 

63 

257.3 

54-7 

24 

23-5 

5-° 

84 

82.2 

17-5 

44 

140.9 

29.9 

04, 

199.5 

42-4 

64 

258.  2 

54-9 

25 

24.5 

5-2 

85 

83- 

'7-7 

45 

141.8 

30.1 

°5 

200.  5 

42.  6 

65 

259.2 

55-  1 

2O 

25.4 

5-4 

86 

84. 

17.9 

46 

142.8 

3°-4 

06 

201.  5 

42.8 

66 

260.  2 

55-3 

27 

26.4 

5-6 

87 

85- 

1  8.  i 

47 

143-8 

30.  6 

°7 

202.  5 

43-° 

67 

26l.  2 

55-5 

28 

27.4 

5-8 

88 

86. 

'8-3 

48 

144-8 

30.8 

08 

203-5 

43-2 

68 

262. 

55-7 

29 

28.4 

6.  o 

89 

87- 

18.5 

49 

MS-  7 

3'-° 

09 

204.4 

43-5 

-69 

263. 

55-9 

3° 

29-3 

6.2 

90 

83.o 

18.7 

5° 

1-46.  7 

31.2 

IO 

205.4 

43-7 

70 

264. 

56.1 

3' 

3°-3 

6.4 

91 

89.0 

18.9 

"5» 

147-7 

3i-4 

211 

206.4 

43-9 

271 

265. 

56-3 

32 

.31-3 

6-7 

92 

90.  o 

19.  i 

52 

148-7 

31.6 

12 

207.4 

44-  l 

72 

266. 

56.6 

33 

32.3 

6.9 

93 

91.0 

'9-3 

53 

'49-  7 

31-8 

'3 

208.3 

44-3 

73 

267.  o 

56.8 

34 

33-3 

7-1 

94 

91.9 

»9-5 

54 

150.  6 

32.0 

H 

209.3 

44-5 

74 

2&8.0 

57-o 

35 

34-2 

7-3 

95 

92-9 

19.8 

55 

151.  6 

32.2 

'5 

210.  3 

44-7 

75 

269.  o 

57-2 

36 

35-2 

7-5 

96 

93-9 

20.  O 

5° 

152.  6 

32-4 

16 

211.3 

44-9 

76 

270.  o 

57-4 

37 

36.2 

7-7 

97 

94-9 

20.  2 

57 

'53-6 

32.6 

17 

212.  3 

45-1 

77 

270.9 

57-6 

33 

37-2 

7-9 

98 

95-9 

20.4 

58 

154.5 

32-9 

18 

213.2 

45-3 

78 

271.9 

57-8 

39 

38-1 

8.  i 

99 

96.8 

20.  6 

59 

'55-5 

33-' 

'9 

214.  2 

45-5 

79 

272.9 

58.0 

40 

39-1 

8-3 

ICO 

97-8 

20.  8 

60 

156-5 

33-  3 

20 

215.2 

45-7 

80 

273-9 

58.2 

4' 

40.  i 

8.5 

101 

98.8 

21.  0 

161 

157-5 

33-5 

221 

2l6.  2 

45-9 

281 

274-9 

58-4 

42 

41.1 

8-7. 

02 

99.8 

21.2 

62 

158.5 

33-7 

22 

217.  I 

46.  2 

82 

275.8 

58.6 

43 

42.  i 

8-9 

03 

loo.  7 

21.4 

63 

159.4 

33-9 

23 

2iS.  I 

40.4 

83 

276.8 

58.8 

44 

43-  ° 

9-  i 

04 

101.  7 

21.6 

04 

160.  4 

34-1 

24 

219.  I 

46.6 

84 

277.8 

59.0 

45 

44.0 

9-4 

°5 

102.  7 

21.8 

65 

161.4 

34-3 

25 

220.  I 

46.  ft 

85 

278.8 

59-3 

46 

45.0 

9.6 

06 

i°3-7 

22.  O 

66 

162.4 

34-5 

26 

221.  I 

47.0 

86 

279.8 

59-5 

47 

46.  o 

9.8 

07 

104.  7 

22.  2 

07 

163.4 

34-7 

27 

222.  O 

47.  2 

87 

280.  7 

59-7 

48 

47.0 

10.  o 

08 

105-7 

22.5 

68 

164.3 

34-9 

28 

223,  o 

47-4 

88 

281.  7 

59-9 

49 

47-9 

IO.  2 

09 

106.  6 

22.  7 

69 

'65.3 

35-' 

29 

224.  o 

47-6 

89 

282.  7 

60.  i 

5° 

48.9 

10.  4 

IO 

107.  6 

22.9 

70 

166.  3 

35-3 

3° 

225.  o 

47-8 

90 

283-7 

60.  3 

51 

49-9 

10.  t> 

III 

108.  6 

23-  1 

171 

'67-3 

35-6 

23" 

226.  o 

4!!  o 

291 

284.6 

60.5 

52 

50.9 

10.8 

12 

109.  6 

23-3 

72 

163.2 

35-8 

32 

226.  9 

48.2 

92 

285.6 

60.7 

53 

SI'S 

11.  0 

'3 

no.  5 

23-5 

73 

169.  2 

36.  o 

33 

227.9 

48.4 

93 

286.6 

60.  9 

54 

52.8 

II.  2 

'4 

in.  5 

23-7 

74 

I7O.  2 

36.2 

34 

228.9 

48.7 

94 

287.6 

61.1 

55 

53-8 

II.  4 

15 

112.5 

23-9 

75 

I7I.2 

36-4 

35 

229.  9 

48.9 

95 

288.6 

6'-3 

56 

54.8 

II.  6 

IO 

"3-5 

24.  I 

76 

?72.2 

36.6 

36 

230.8 

49-  I 

96 

289-5 

oi.  5 

57 

55-8 

II.  9 

'7 

114.4 

24.3 

77 

173-1 

36.8 

37 

231.8 

49-3 

97 

290.5 

61.7 

53 

50.7 

12.  I 

18 

115.4 

24.5 

/8 

174.  i 

37-o 

38 

232.8 

49-5 

98 

291-5 

62.0 

59 

57-7 

12.3 

19 

110.4 

24.  7 

79 

175.1 

37.2 

39 

233.8 

49-  7 

99 

292.5 

62.2 

60 

58.7 

12.5 

20 

117.4 

24.9 

So 

176.1 

37-4 

40 

234.8 

49-9 

300 

293-4 

62.4 

Dlst. 

Dap. 

Lat. 

Dlst. 

Dop. 

Lat. 

Dlst. 

Dep 

Lat. 

Dl»t, 

Dep. 

Lat. 

Dist. 

Dep 

Lat. 

[For  78  Degrees. 

125 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  13°. 

Ilist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

I 

I.o 

0.  2 

61 

59-4 

13-7 

121 

II7.9 

27.2 

181 

176.4 

40.  7 

241 

234.8 

54-2 

2 

1.9 

0.4 

62 

00.4 

13-9 

22 

118.9 

27.4 

82 

177-3 

40.9 

42 

235-8 

54-4 

3 

2.9 

o.  7 

63 

61.4 

14.2 

23 

II9.8 

27.7 

83 

178.3 

41.2 

43 

236.8 

54-7 

4 

3-9 

0.9 

64 

62.  4 

14.4 

24 

120.  & 

27.9 

84 

179-3 

41.4 

44 

237-7 

54-9 

5 

4-9 

I.  I 

65 

63-3 

14.  6 

25 

121.  8 

23.  I 

85 

180.3 

41.  6 

45 

238.7 

55-1 

6 

5-8 

1.3 

66 

64-3 

14.8 

26 

122.8 

28.3 

86 

181.2 

41.8 

46 

239.7 

55-3 

7 

6.8 

1.6 

67 

65.3 

15.  i 

27 

123.7 

28.6 

87 

182.2 

42.1 

47 

240.7 

55-6 

8 

7-8 

1.8 

68 

66.3 

15-3 

23 

124.7 

28.8 

88 

183.2 

42-3 

48 

241.  6 

55-8 

9 

8.8 

2.  O 

69 

67.2 

15-5 

?9 

125.7 

29.  o 

89 

184.  2 

42.5 

49 

242.6 

56.  o 

10 

9-7 

2.  2 

70 

68.2 

15-7 

3° 

126.  7 

2Q.  2 

90 

185.  I 

<2.7 

50 

243.6 

56-2 

II 

10.7 

2-5 

7« 

69.  2 

16.  o 

I31 

127.6 

29.5 

191 

1  86.  i 

43-° 

251 

244.6 

56.5 

12 

n.  7 

2.7 

72 

70.2 

16.2 

32 

128.6 

29-7 

92 

187.  i 

43-2 

52 

245-5 

56.7 

13 

12.7 

2.9 

73 

7I.I 

16.  4 

33 

129.  6 

29.9 

93 

iSS.  i 

43-4 

53 

246.5 

56.9 

>4 

13.6 

3-> 

74 

72.1 

16.6 

34 

130.  6 

30.1 

94 

189.0 

43-6 

54 

247-5 

57-1 

15 

14.  6 

3-4 

75 

73-1 

16.9 

35 

13I-5 

3°-4 

95 

190.0 

43-9 

55 

248.5 

57-4 

16 

15.6 

3-6 

76 

74-1 

17.1 

S6 

132-5 

30.  6 

96 

191.  o 

44.  i 

56 

249-4 

57-6 

17 

16.  6 

3-8 

77 

75-o 

17-3 

37 

133-5 

30.8 

97 

192.0 

44-3 

57 

250.4 

57-8 

18 

'75 

4.0 

78 

76.0 

17-5 

38 

134-5 

31.  o 

98 

192.9 

44-5 

58 

251.4 

58.0 

19 

18.5 

4-3 

79 

77.0 

17.8 

39 

135-4 

3'-3 

99 

i'93-  9 

44-8 

59 

252.4 

58.3 

20 

'9-5 

4-5 

80 

77-9 

18.  o 

40 

136.4 

31-5 

200 

194.9 

45-° 

60 

253-3 

58-5 

21 

20.  5 

4-7 

81 

78.9 

1  8.  2 

141 

137-4 

3'-7 

201 

195.8 

45.2 

261 

254.3 

58.7 

22 

21.4 

4-9 

82 

79-9 

18.4 

42 

138.4 

3'-  9 

O2 

196.8 

45-4 

62 

255-  3 

58.9 

23 

22.4 

5-2 

83 

80.9 

18.7 

43 

139-3 

32.2 

°3 

197-8 

45-7 

63 

256.3 

59-2 

24 

23-4 

5-4 

84 

81.8 

18.9 

44 

140-3 

32-4 

04 

198.8 

45-9 

64 

257-2 

59-4 

25 

24.4 

5-6 

85 

82.8 

19-  l 

45 

141-3 

32.  6 

°5 

199-7 

46.  i 

65 

258.2 

59-6 

26 

25-3 

5-8 

86 

83.8 

19-3 

46 

142.3 

32.3 

06 

200.  7 

46-3 

66 

259.2 

59-8 

27 

26.3 

6.  i 

87 

84.8 

19.6 

47 

143.2 

33-' 

07 

201.  7 

46.  6 

67 

260.2 

60.  i 

28 

27-3 

6-3 

88 

85.7 

19.8 

48 

144.2 

33-3 

08 

202.  7 

46.8 

68 

261.  i 

60.3 

29 

28.3 

6-5 

89 

86.7 

20.  O 

49 

145.2 

33-5 

09 

203.  6 

47.0 

69 

262.  i 

60.  5 

3° 

29.  2 

6-7 

90 

87.7 

20.  2 

5° 

146.  2 

33-7 

10 

204,  6 

47-2 

70 

263.  i 

60.  7 

31 

30.2 

7.0 

9' 

88.7 

20.5 

»5i 

I47.I 

34-0 

211 

205.  6 

47-5 

271 

264.  i 

61.  o 

32 

31.2 

7.2 

92 

89.6 

20.  7 

S2 

148.  I 

34-2 

12 

206.  6 

47-7 

72 

265.  o 

61.2 

33 

32.2 

7-4 

93 

90.  6 

20.  9 

53 

149.  I 

34-4 

'3 

207.5 

47-9 

73 

266.0 

61.4 

34 

33-' 

7-6 

•94 

91.  6 

21.  I 

54 

150.  I 

34-6 

14 

208.  5- 

48.  i 

74 

267.  o 

61.6 

35 

34-1 

7-9 

95 

92.  6 

21.4 

55 

151.  o 

34-9 

15 

209.5 

48.4 

75 

268.0 

61.  9 

36 

35-i 

8.1 

96 

93-5 

21.6 

56 

152.  o 

35-1 

16 

210.  5 

48.6 

76 

268.9 

62.1 

37 

36.1 

8-3 

97 

94-5 

21.8 

57 

153.0 

35-3 

17 

211.4 

48.8 

77 

269.9 

62.3 

3S 

37-0 

8-5 

98 

95-5 

22.  O 

58 

154.0 

35-5 

18 

212.  4 

49.0 

78 

270.9 

62.5 

39 

38.0 

8.8 

99 

96.5 

22.3 

59 

154.9 

35-8 

19 

213-4 

49-3 

79 

271.8 

62.8 

40 

39-° 

9.0 

100 

97-4 

22.5 

60 

155-9 

36.  o 

20 

214.4 

49-5 

80 

272.8 

63.  o 

41 

39-9 

9.2 

101 

98:4 

22.7 

161 

156.9 

36.2 

221 

215-3 

49-  7 

281 

273-8 

63.2 

42 

40.9 

9-4 

02 

99-4 

22.9 

62 

157.8 

36.4 

22 

216.  3 

49-9 

82 

274.8 

6>4 

43 

41.9 

9-7 

°3 

100.4 

23.  2 

63 

158.8 

36.7 

23 

217-3 

50.2 

83 

275-7 

63.7 

44 

42.9 

9.9 

04 

101.3 

23-4 

64 

159.8 

36-9 

24 

218.3 

5°-4 

84 

276-7 

63-9 

45 

43-8 

10.  I 

°5 

102.3 

23-6 

65 

160.8 

37-1 

25 

219.  2 

50.  6 

85 

277.7 

64.1 

46 

44.8 

10.  3 

06 

i°3-3 

23-8 

66 

161.  7 

37-3 

26 

22O.  2 

50.8 

86 

278.7 

64-3 

47 

45-8 

10.6 

07 

104.3 

24.  I 

67 

162.7 

37-6 

27 

221.2 

51.1 

87 

279.6 

64.6 

48 

46.8 

10.8 

08 

105.  2 

24-3 

68 

l63-7 

37-8 

28 

222.  2 

5'-3 

88 

280.6 

64.8 

49 

47-7 

II.  O 

09 

1  06.  2 

24-5 

69 

164.  7 

38.0 

29 

223.  I 

5'-5 

89 

281.6 

65.  o 

5° 

48.7 

II.  2 

:o 

107.  2 

24.7 

70 

165.6 

38.2 

3° 

224.  I 

51-7 

90 

282.6 

65.  2 

51 

49-  7 

ii-5 

in 

1  08.  2 

25.  o 

171 

166.  6 

3«-S 

231 

225.1 

52-0 

291 

283.5 

65.5 

52 

5°-7 

n.  7 

12 

log.  I 

25.2 

72 

167.6 

38.7 

32 

226.  I 

52.2 

92 

284.5 

65.7 

53 

51.6 

u.  9 

13 

I  10.  I 

25.4 

73 

168.6 

38.9 

33 

227.  o 

52.4 

93 

285.5 

65.9 

54 

52-6 

12.  I 

'4 

III.  I 

25.6 

74 

169.5 

39-1 

34 

228.0 

52-6 

94 

286.5 

66.  i 

55 

53-6 

12.4 

15 

112.  I 

25.9 

75 

>7o.5 

39-4 

35 

229.  o 

52.9 

95 

287.4 

66.4 

56 

54-6 

12.6 

16 

113.  o 

26.  I 

76 

171.5 

39-6 

36 

230.  o 

53-1 

96 

288.4 

66.6 

57 

55-5 

12.8 

'7 

114.  o 

26.3 

77 

172.5 

39-8 

37 

230.9 

53-3 

97 

289.4 

66.8 

58 

56.5 

13.0 

18 

II5.0 

26.  5 

78 

173-4 

40.  o 

38 

231-9 

53-5 

98 

290.4 

67.  o 

59 

57-5 

13.3 

39 

u6.  o 

26.8 

79 

174-4 

40.3 

39 

232.9 

53-8 

99 

291.3 

67.3 

60 

58.5 

13.5 

20 

116.9 

27.0 

80 

175-4 

40.5 

40 

233.8 

54.0 

300 

292.3 

67.5 

Dist. 

Dcp. 

Lat. 

Dist. 

"Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[For  77  Degrees. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  14°. 

Dlst. 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

Ulsl. 

tut 

Dep. 

I 

I.  O 

O.  2 

61 

59-2 

14.  8 

121 

II7.4 

29-3 

181 

175-6 

43-  * 

241 

233-  s 

58-3 

2 

1.  9 

0.5 

62 

60.  2 

15-0 

22 

118.4 

29.  5 

82 

176.  6 

44.0 

42 

234-8 

5s-  5 

3 

2.9 

0.7 

63 

61.  i 

15-2 

23 

"9-  3 

29.8 

83 

177.6 

44-  3 

43 

235.  8 

58  J 

4 

3-9 

.  O 

64 

62.  I 

'5-5 

24 

120.  3 

30.0 

84 

178.5 

44-  5 

44 

230.  8 

50.  o 

5 

4-9 

.2 

63.1 

"5-7 

25 

121.3 

30.  2 

85 

'79-  5 

44.8 

45 

237-  7 

5*  3 

6 

5-8 

•5 

66 

64.  o 

16.  o 

26 

122.3 

3°-5 

So 

180.  5 

45.0 

46 

238.  7 

5*5 

7 

6.8 

•  7 

67 

65.  c 

16.  2 

27 

123.2 

3?-  7 

87 

181.4 

45-2 

47 

239-  7 

59.8 

8 

7-8 

•9 

68 

65.o 

16.5 

28 

124.  2 

31.0 

88 

182.4 

45-5 

48 

240.  6 

bo.  o 

9 

8-7 

2.  2 

69 

67.  o 

16.7 

29 

135.2 

89 

183.4 

45-  7 

49 

241.  6 

60.  2 

10 

9-7 

2.4 

70 

67-9 

1  6.  9 

30 

126.  1 

3'-4 

90 

(84.  4 

46.  o 

5° 

242.  6 

60.5 

ii 

10.7 

2-  7 

7' 

68.9 

17.2 

'3' 

127.  1 

3'-7 

191 

185.3 

46.  2 

251 

243-  5 

60.  7 

12 

n.  6 

2.9 

72 

69.9 

17.4 

32 

128.  1 

3'-9 

92 

186.3 

46.4 

S2 

244-  5 

61.  o 

»3 

12.6 

3-1 

73 

70.8 

'7-7 

33 

129.  o 

32-2 

93 

'87.3 

46.7 

53 

245-5 

61.  i 

>4 

13-6 

3-4 

74 

71.8 

17-9 

34 

130.0 

32-4 

94- 

188.2 

46.9 

54 

246.  5 

61.4 

'5 

14.6 

3-6 

75 

72.8 

18.  i 

35 

131.0 

32-7 

95 

I8g.  2 

47-2 

55 

247-4 

Oi.7 

16 

>5-5 

3-9 

76 

73-7 

18.4 

36 

132.0 

32.9 

96 

190.  2 

47-4 

5s 

248.4 

61.  9 

'7 

16.5 

4.1 

77 

74-7 

18.6 

37 

132.9 

33-' 

97 

191.  I 

47-  7 

57 

249.  4 

62.2 

iS 

'7-5 

•4.4 

78 

75-7 

18.9 

38 

'33-9 

33-4 

98 

192.  I 

47-9 

25"-  3 

62.4 

19 

18.4 

4.6 

Z9 

76.7 

19.1 

39 

'34-9 

33-6 

99 

193-  « 

48.  i 

59 

25'-3 

62.  7 

20 

19.4 

4-8 

80 

77-6 

19.4 

40 

'35-8 

33-9 

200 

194.  I 

48.4 

60 

252.  1 

62.  9 

21 

20.4 

5-  ' 

81 

78.6 

19.  6 

141 

136.8 

34-1 

201 

195-0 

48.6 

201 

253.  2 

63.1 

22 

21.3 

5-3 

82 

79.6 

19.8 

42 

137-8 

34-4 

O2 

196.  o 

48.9 

63 

254.  2 

63.4 

23 

22.3 

5-6 

83 

80:5 

20.  i 

43 

138.8 

34-6 

°3 

197.0 

49.1 

63 

255-2 

63.  6 

24 

23-3 

5-8 

84 

81.5 

20.3 

44 

'39.  7 

34-8 

04 

197-9 

49-4 

64 

256.  2 

63.9 

25 

24-3 

6.  o 

85 

82.5 

20.  6 

45 

MO.  7  . 

35-  i 

°5 

198.9 

49-6 

65 

257.  1 

64.  i 

26 

25.  2 

6-3 

86 

83-4 

20.8 

46 

141.  7 

35-3 

06 

199.9 

49-8 

66 

25!  I 

64-4 

27 

26.  2 

6-5 

87 

84.4 

21.  O 

47 

142.  6 

35-6 

°7 

200.  9 

50.1 

67 

259.  I 

64.6 

28 

27.  2 

6.8 

88 

85.4 

21-3 

48 

M3-6 

35-8 

08 

201.8 

50.3 

68 

260.  o 

64.8 

29 

28.  I 

7-0 

89 

86.4 

21.  5 

49 

144.6 

36.  o 

09 

202.8 

50.  6 

69 

261.  o 

65.1 

3° 

29.1 

7-3 

90 

87.3 

21.8 

50 

«45-5 

36.3 

10 

203.3 

50.  8 

26-!.  o 

65.3 

3' 

30.1 

7-5 

9' 

88.3 

22.  O 

'5' 

146.5 

36-5 

211 

204.  7 

51.0 

271 

263.  o 

65.6 

32 

31.0 

7-7 

92 

89-3 

22.3 

52 

M7-  5 

36.8 

12 

205.7 

5'-3 

72 

263.9 

6s.  8 

33 

32.0 

8.0 

93 

90.  2 

22.5 

53 

148.5 

37-0 

'3 

206.  7 

73 

264.  9 

G6.  o 

34 

33-0 

8.2 

94 

91.2 

22.7 

54 

149.4 

37-3 

M 

207.  f> 

s!J 

74 

265.9 

C6.  3 

35 

34-0 

8-5 

95 

92.  2 

23.  o 

55 

150.4 

37-5 

15 

208.6 

52.0 

75 

266.  8 

66'.  5 

36 

34-9 

8:7 

96 

93-  i 

23.  2 

56 

'5>-4 

37-7 

16 

209.  6 

52.3 

76 

2&7.S 

66.8 

35-9 

9.0 

97 

94.1 

23-5 

5Z 

152.  3 

38.0 

'7 

2IO.  6 

52.5 

77 

263.  & 

67.  o 

$ 

9.2 

98 

95-  ' 

23-7 

58 

'53-3 

38-2 

18 

211.5 

52.7 

269.  7 

67.3 

39 

37-  8 

9-4 

99 

96.1 

24.  o 

59 

154.3 

38.5 

'9 

212.  S 

53-° 

79 

270.  7 

67.5 

40 

38.8 

9-7 

ICO 

97.0 

24.2 

60 

155.2 

38.7 

20 

213-5 

53-2 

80 

271.  7 

67.7 

4' 

39-8 

9-9 

101 

98.0 

24.4" 

161 

156.  2 

3«-9 

221 

214,4 

53-5 

zSi 

272.  7 

68.  o 

42 

40.8 

10,2 

02 

99.0 

24.7 

62 

157.2 

39-2 

22 

215.4 

53.  7 

82 

273-  6 

63.2 

43 

41.7 

10.4 

03 

9?-  9 

24-9 

63 

IS8.2 

39-4 

23 

216.  4 

53-9 

83 

274.6 

63.  5 

44 

42-7 

10.  6 

04 

100.9 

25.2 

64 

I59.I 

39-  7 

24 

217.3 

54-2 

84 

275.6 

C8.  7 

45 

43-7 

10.  9 

OS 

101.9 

25.4 

65 

1  60.  I 

39-9 

25 

218.  3 

54-4 

85 

2/6,5 

03.9 

46. 

44.  6 

II.  I 

06 

102.  0 

25.  6 

66 

161.  i 

40.  2 

26 

219-3 

54-7 

86 

69.2 

47 

45-6 

11.4 

°z 

103.8 

25.9 

67 

162.  o 

40.4 

27 

220.3 

54-9 

87 

278.  5. 

69.4 

43 

46.6 

M.  6 

08 

104.  8 

26.  i 

68 

163.  o 

40.  6 

28 

221.  2 

55-2 

83 

279-4 

69-7 

49 

47-5 

11.9 

09 

105.8 

26.  4 

69 

164.  o 

40.9 

29 

222.  2 

55'.  4 

89 

280.4 

69.9 

50 

48.5 

12.  I 

10 

1  06,  7 

26.6 

7° 

165.  o 

41.1 

223.2 

55.  6 

90 

sSl.  4 

70.  2 

5' 
52 

49-5 
So.S 

12.  3 

12.6 

III 

IZ 

107.7 
108.  7 

26.  9 
27.1 

72 

165.5 
166,9 

41.4 
41.  6 

23' 
32 

224*  I 
225.1 

55-9 
56.1 

291 
92 

282.4 
283-3 

7°-  4 
70.  6 

53 

S'-4 

12.8 

«3 

loo.  6 

27-3 

73 

167.9 

41.  3 

33 

226.  I 

56.4 

93 

284.3 

70.9 

54 

52.4 

'3-1 

'4 

I  to.  6 

27.  6 

74 

l6u.  0 

42.  i 

34 

S27.  0 

56.6 

94 

285.3 

71.1 

55 

53-4 

'3-3 

15 

in.  6 

27.8 

169.8 

42-3 

35 

228.  o 

56.9 

2  86.  -2 

71.4 

5§ 

54-3 

'3-5 

16 

us.  6 

28.1 

70 

170.8 

42.  6 

30 

229.O 

57-1 

96 

287.  2 

71.  6 

57 

55-3 

13.8 

17 

"3-5 

28.3 

77 

171.7 

42.8 

37 

230.0 

57-3 

97 

288.2 

71.9 

58 

56.3 

It..  0 

18 

"4-5 

28.5 

173.  7 

43-  « 

38 

250*  9 

57-6 

96 

289.  I 

72.  I 

59 
60 

57-2 
5$.  a 

H-3 
14.5 

'9 

20 

"S-S 
no,  4 

28.8 
20.  0 

ll 

I73.7 
174-7 

43-3 
43-5 

39 
4o 

232.9 

12:? 

99 
300 

290.  I 
291.  I 

7*0 

Dlst. 

Dep.   . 

Lat. 

Dlst. 

Dep. 

Lat.    I  Dlst. 

Dep, 

Lat. 

bist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  76  Degrees. 

L£t 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  15°. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

I.O 

0-3 

61 

58.9 

I5.8 

121 

1  16.  9 

31-3 

181 

174.8 

46.8 

241 

232.8 

62.4. 

2 

1.9 

o.  5 

62 

59-9 

16.  o 

22 

117.8 

31-6 

82 

175-8 

47-1 

42 

233-8 

62.6 

3 

2.9 

0.8 

63 

60.9 

'6-3 

23 

118.8 

31-8 

83 

176.8 

4;.  4 

43 

234.7 

62.  9 

4 

•3,  O 

I.O 

64 

61.8 

16.  6 

24 

119.8 

32-  I 

84 

177-7 

>7-6 

44 

235-7 

63.2 

5 

A,  O 

"•3 

65 

62.8 

16.  8 

25 

120.7 

32-4 

85 

178.7 

47-9 

45 

236.  7 

63-4 

6 

5-8 

1.6 

66 

63.8 

17.1 

26 

121.7 

32-6 

86 

179-7 

48.  I 

46 

237.6 

63.7 

7 

6.8 

1.8 

67 

64.7 

'7-3 

27 

122.7 

32-9 

87 

i  Go.  6 

48.4 

47 

238.6 

63-9 

8 

7-7 

2.  I 

68 

65.7 

17.6 

28 

123.  6 

33-  i 

88 

181.6 

48.7 

48 

239.5 

64,  2 

9 

8.7 

2-3 

69 

66.6 

17.9 

29 

124.  6 

33-4 

89 

182.6 

48.9 

49 

240.5 

64.4 

10 

9-7 

2.6 

70 

67.6 

i&.i 

3° 

125.  6 

33-6 

90 

183-5 

49-  2 

5° 

24L5 

64.7 

ii 

10.  6 

2.8 

71 

68.6 

18.4 

'3' 

ic6.5 

33-9 

191 

184-5 

49-4 

25> 

242.4 

65.0 

12 

11.  6 

3-  i 

72 

69.5 

18.  6 

32 

127-5 

34-2 

92 

185.5 

49-7 

52 

243-4 

65.2 

13 

12.  6 

3-4 

73 

7o-5 

1  8.  9 

33 

128.5 

34-4 

93 

186.4 

50.  o 

53 

244-4 

65-5 

14 

"3-5 

3-6 

74 

7L5 

19.2 

34 

129.4 

34-7 

94 

187-4 

50.  2 

54 

245-3 

65-7 

15 

H.5 

3-9 

75 

72.4 

19.4 

35 

J3°-4 

34-9 

95 

188.4 

5°-5 

55 

246.3 

66.0 

16 

'5-5 

4-1 

76 

73-4 

19.7 

j6 

131-4 

35-2 

96 

189-3 

50.7 

56 

247-3 

66.3 

17 

16.4 

4-4 

77 

74-4 

19.9 

37 

132.3 

35-5 

97 

190.3 

51.0 

57 

248.2 

65.  5 

Io 

17.4 

4-7 

78 

75-3 

2O.  2 

38 

133-3 

35-7 

98 

191-3 

51-2 

58 

249.2 

66.8 

19 

18.4 

4-9 

79 

76.3 

20-4 

39 

134-3 

36.  o 

99 

192.  2 

51-5 

59 

250.  2 

67.  o 

20 

'9-3 

5-2 

So 

77-3 

20.  7 

40 

'35-  2 

36.  2 

200 

193.2 

5I.S 

60 

25I.I 

67.3 

21 

20.3 

5-4 

Si 

78.2 

21.  O 

141 

136.  2 

30-5 

201 

194-2 

52.0 

261 

252.  I 

67.6 

22 

21.3 

5-7 

82 

79.2 

21.  2 

42 

137-2 

36.8 

O2 

I95.I 

52-3 

62 

253-  1 

67.8 

23 

22.  2 

6.  o 

83 

80;2 

2I.S 

43 

I3S.I 

37-0 

°3 

196.  I 

52.5 

63 

254.0 

68.  i 

24 

23.2 

6.2 

84 

81.  i 

21.7 

44 

139.  I 

37-3 

04 

197.0 

52.8 

64 

255-P 

68.3 

25 

24.  I 

6-5 

85 

82.1 

22.  0 

45 

140.  I 

37-5 

05 

198.  o 

53-1 

65 

256.0 

68.6 

26 

25-1 

6.7 

E6 

83.1 

22.3 

46 

141.  o 

37-8 

06 

199.0 

53-3 

66 

256.9 

68.8 

27 

26.  I 

7.0 

87 

84.0 

22.  5 

47 

142.  o 

38.0 

°7 

199.9 

53-6 

67 

257.9 

69.  i 

28 

27.  o 

7-2 

88 

85.  o 

22.8 

43 

143.0 

38.3 

08 

200.  9 

53-8 

68 

258.  9 

69-4 

29 

28.0 

7-5 

89 

86.  o 

23.  o 

49 

143.9 

38.6 

09 

201.  9 

54-i 

69 

259-8 

69.6 

3° 

29.  o 

7-8 

90 

86.9 

23-3 

5° 

144.9 

33.8 

10 

202.  8 

54-4 

70 

260.  8 

69.9 

3' 

29.9 

8.0 

91 

87.9 

23.  6 

151 

145.9 

39-1 

211 

203.8 

54-6 

271 

261.8 

70.1 

32 

3°-9 

8-3 

92 

88.9 

23.8 

52 

146.8 

39-3 

12 

204.8 

54-9 

72 

262.  7 

70.4 

33 

3'-9 

8.5 

93 

89.8 

.24-  i 

53 

147.8 

39-6 

13 

205.7 

55-  « 

73 

263-7 

70.7 

34 

32.8 

8.8 

94 

90.8 

24.  3 

54 

148.8 

39-9 

14 

206.  7 

55-4 

74 

264.7 

70.9 

35 

33-8 

9-i 

95 

91.8 

24.6 

55 

149.7 

40.  i 

15 

207.7 

55-6 

75 

265.6 

71.2 

36 

34-8 

9-3 

96 

92.7 

24.8 

56 

150.  7 

40.4 

16 

208.6 

55-9 

76 

266.6 

71.4 

37 

35-7 

9.6 

97 

93-7 

25.1 

57 

'Si-? 

40.  6 

17 

209.  6 

56.2 

77 

267.  6 

71-7 

38 

36-7 

9-8 

98 

94>7 

25-4 

58 

152.  6 

40.9 

18 

210.  6 

56-4 

78 

268.5 

72.0 

39 

37-7 

10.  I 

99 

95.6 

25.  6 

59 

'53-6 

41.2 

19 

211.  5 

56.7 

79 

269.5 

72.  2 

40 

38.6 

10.4 

IOO 

96.6 

25-9 

60 

154.5 

41.4 

20 

212.5 

56.9 

80 

270.5 

72-5 

41 

39-6 

10.  6 

101 

97-6 

26.  i 

161 

•55-5 

4i-7 

221 

213-5 

57-2 

281 

271.4 

72.7 

42 

40.  6 

10.  9 

02 

98.5 

26.  4 

62 

156.5 

41.9 

22 

214.4 

57-5 

82 

272.4 

73-0 

43 

41.5 

ii.  i 

°3 

99-5 

26.  7 

63 

157.4 

42.2 

23 

215.4 

57-7 

83 

273-4 

73-2 

44 

42-5 

11.4 

04 

loo.  5 

26.  9 

64 

158.4 

42.4 

24 

216.  4 

58.0 

84 

274-3 

73-5 

45 

43-5 

ii.  6 

05 

101.4 

27.2 

65 

159-4 

42.7 

25 

217.3 

58.2 

85 

275-3 

73-8 

46 

44-4 

11.9 

06 

102.  4 

27.4 

66 

160.3 

43-0 

26 

218.3 

58.5 

86 

276.3 

74.0 

47 

45-4 

12.  2 

°7 

l°3-4 

27.7 

67 

161.  3 

43-2 

27 

219.3 

58.8 

87 

277.  2 

74-3 

48 

46.4 

12.4 

08 

104-3 

28.0 

68 

162.  3 

43-5 

28 

22O.  2 

59-0 

88 

278.2 

74-5 

49 

47-3 

12.7 

09 

l°5-  3 

28.2 

69 

163.  2 

43-7 

29 

221.  2 

59-3 

89 

279.2 

74-8 

5° 

4S.3 

12.9 

Io 

106.3 

28.5 

70 

164.  2 

44.0 

3°" 

222.  2 

59-5 

90 

280.  I 

7S-I 

5i 

49-3 

13-2 

in 

107.  2 

28.7 

I7i 

165.2 

44-3 

231 

223.  I 

59.8 

291 

28l.  I 

75-3 

52 

50.  2 

'3-5 

12 

108.  2 

29.  o 

72 

1  66.  i 

44-5 

32 

224.  I 

60.  o 

92 

282.  I 

75.6 

53 

51.2 

'3-7 

'3 

109.  I 

29.2 

73 

167.  i 

44-8 

33 

225.  I 

60.3 

93 

283.0 

75-8 

54 

52.  2 

14.0 

14 

1  10.  I 

29.5 

74 

1  68.  i 

45.0 

34 

226.  o 

60.  6 

94 

284.0 

76.1 

55 

53-i 

14.2 

15 

III.  I 

29.8 

75 

169.  o 

45-3 

35 

227.  o 

60.8 

95 

284.9 

76.4 

56 

54-1 

14-5 

IO 

1  12.  b 

30.0 

76 

170.  o 

45-  6 

36 

228.0 

61.  i 

96 

285.9 

76.6 

57 

55-1 

14.8 

17 

113.0 

30.3 

77 

171.0 

45;  8 

37 

228.9 

61.3 

"97 

286.9 

76.9 

58 

56.0 

15.0 

18 

114.  o 

30.5 

78 

171.9 

46.  i 

38 

229.9 

61.6 

98 

287.8 

77-1 

59 

57-0 

'5-3 

19 

114.9 

30.8 

79 

172.9 

46-3 

39 

230.  9 

61.9 

99 

288.8 

77-4 

60 

58.0 

'5-5 

20 

115.9 

3I.I 

So 

173-9 

46.6 

40 

231.8 

62.  i 

300 

289.8 

77-6 

Dlst. 

Dop. 

Let. 

Pitt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[For  75  Degrees. 

128 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  10°. 

Dist 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

1 

1.0 

°-  3 

6i 

58.6 

16.  8 

121 

1  16.  3 

33-4 

181 

174.0 

49-9 

24  1 

231.7 

66.4 

2 

'•9 

0.6 

62 

59-6 

17.  I 

22 

"7-3 

33-6 

82 

174-  9 

50.2 

42 

232.  6 

66.7 

3 

2.  Q 

0.8 

63 

60.6 

«7-4 

23 

1:8.2 

33-9 

83 

175-9 

5°-4 

43 

233.  6 

67.0 

4 

3-8 

I.  I 

64 

61.5 

17.6 

24 

119.  2 

34-2 

84 

176.9 

50.7 

44 

234-S 

67.3 

5 

4-8 

1.4 

65 

62.5 

>7-9 

25 

1  2O.  2 

34-5 

85 

177.8 

5>-° 

45 

235-5 

67.5 

I 

5-8 

1.7 

66 

63.4 

IS.  2 

26 

121.  I 

34-7 

86 

178.8 

5>-3 

46 

236-5 

67  J 

7 

6.7 

'•9 

67 

64.4 

18.5 

27 

122.  I 

35-0 

87 

179.8 

5'-  5 

47 

237-4 

68.1 

8 

7-7 

2.2 

63 

65.4 

iS-7 

28 

123.0 

35-3 

88 

180.7 

51.8 

48 

238-4 

68.4 

9 

8.7 

2.  5 

69 

66.3 

19.  o 

29 

124.  o 

35-6 

89 

181.  7 

52.1 

49 

239-4 

68.6 

10 

9.6 

2.8 

70 

67.3 

'9-  j 

3° 

125.  o 

35-  8 

90 

182.6 

52.4 

5° 

240.3 

68.9 

11 

10.  6 

3-  ° 

7' 

68.2 

19.  6 

'3' 

125.9 

36.1 

191 

183.6 

52.0 

251 

241-3 

69.2 

12 

"•5 

3-3 

72 

69.  2 

19.8 

32 

126.  9 

36.4 

92 

184.6 

52.9 

52 

242.  2 

69.5 

'3 

12.5 

f 

3.6 

73 

70.2 

20.  i 

33 

127.8 

36.7 

93 

185.5 

S3-2 

53 

243.2 

69.7 

14 

'3-5 

3-9 

74 

7LI 

20.  4 

34 

128.8 

36-9 

94 

186.5 

53-5 

54 

244.2 

70.0 

15 

14.4 

4-  i 

75 

72.1 

20.  7 

35 

129.  8 

37-2 

95 

187.4 

53-7 

55 

245.  I, 

73.3 

16 

•5-4 

4-4 

76 

73-1 

20.  9 

36 

130.7 

37-5 

96 

188.4 

54.0 

56 

246.  I 

70.6 

17 

'6-3 

4-7 

77 

74.0 

21.  2 

37 

131-7 

37-8 

97 

189.4 

54-3 

57 

247.0 

70.8 

ifi 

17-3 

5-° 

78 

75.0 

21.5 

38 

«32.7 

38.0 

98 

190.3 

54.6 

58 

248.  o 

71.1 

'9 

'8-3 

5-2 

79 

75-9 

21.8 

39 

'33-6 

38.3 

99 

'91-3 

54-9 

59 

249.0 

71.4 

20 

19.2 

5-5 

80 

76.9 

22.  I 

40 

'34-6 

38.6 

200 

192-3 

55-' 

60 

249-9 

71-7 

21 

2O.  2 

5-« 

87~1 

77-9 

22.  3 

141 

135-5 

3y-9 

201 

193-2 

55-4 

261 

250.9 

7'-9 

22 

21.  I 

6.1 

82 

78.8 

22.  6 

42 

'36.5 

39-  ' 

O2 

194-2 

55-7 

62 

25L9 

72.2 

23 

22.  I 

6-3 

83 

79-8 

22.  9 

43 

137-5 

39-4 

°3 

195-  i 

56.0 

63 

252.* 

72.5 

24 

23-' 

6.6 

84 

80.  7 

23.  2 

44 

138.4 

39-7 

04 

196.  i 

56.2 

64 

253-8 

72.8 

25 

24.  o 

6.9 

85 

81.7 

23-4 

45 

'39-4 

40.  o 

°5 

197.1 

5!M 

65 

254-7 

73-3 

26 

25.0 

7-2 

86 

82.7 

23-7 

46 

140.3 

40.  2 

06 

198.0 

56.8 

66 

255-7 

73-3 

27 

26.  o 

7-4 

87 

83.6 

24.0 

47 

'4'-3 

40.5 

07 

199.0 

57.' 

67 

256.7 

73-6 

28 

26.  9 

7-7 

88 

84.6 

24-3 

48 

142-3 

40.8 

08 

199.9 

57-3 

68 

257.6 

73-9 

29 

27.9 

8.0 

89 

85.6 

24.5 

49 

J43-2 

41.  1 

09 

200.  9 

57-6 

69 

258.6 

74-  ' 

3° 

28.8 

8-1 

9° 

86.5 

24-8 

50 

144.2 

41.3 

10 

201.  9 

57-9 

70 

259-5 

74-4 

3« 

29.8 

8.5 

91 

87.5 

25.1 

>5' 

145.2 

41.  6 

211 

202.  8 

5o2 

271 

260.  5 

74-7 

32 

30.  8 

8.8 

92 

88.4 

25-4 

S2 

146.  i 

41.9 

12 

203.  8 

58.4 

72 

261  5 

75-0 

33 

3'-7 

9-  ' 

93 

89.4 

25.  6 

S3 

147.1 

42.2 

13 

204.7 

58.7 

73 

262.  4 

75-2 

34 

32-7 

9-4 

94 

90.4 

25.9 

54 

148.0 

42.4 

'4 

205.7 

59.0 

74 

263.4 

75-  5 

35 

33-6 

9-6 

95 

9'-  3 

26.  2 

55 

149.0 

42.7 

IS 

206.  7 

59-3 

75 

264.3 

75-8 

36 

34-6 

9-9 

96 

92-3 

26.5 

56 

150.  o 

43-0 

16 

207.  6 

59-5 

76 

265.3 

76.' 

37 

35-6 

10.  2 

97 

93-  2 

26.  7 

57 

150.9 

43-3 

17 

208.6 

59.8 

77 

266.3 

76.4 

38 

36.5 

10.5 

98 

94.2 

27.  o 

S8 

151.0 

43-6 

18 

209.  6 

60.  i 

7» 

267.  2 

76.6 

39 

40 

37-5 

2LS 

to-  7 

II.  0 

99 

100 

a* 

27'1 
27.  6 

59 

ixj 

152.8 
'53-8 

43-8 
44.  i 

19 

20 

210.  5 
211.  5 

6o.4 
60.6 

79 

80 

268.2 
269.  2 

76.9 

77-2 

4' 

39-4 

"•3 

101 

97-  i 

27.8 

161 

154-8 

44-4 

221 

212.4 

60.  9 

2Sl 

270.  I 

77-5 

42 

40.4 

n.  6 

02 

98.0 

28.  i 

62 

'55-7 

44-  7 

22 

213.4 

61.2 

82 

27I.I 

77-7 

43 

4'-  3 

11.9 

°3 

99.0 

28.4 

63 

156.7 

44-9 

23 

214.4 

61.5 

83 

272.  o 

78.0 

44 

42-3 

12.  I 

04 

100.  o 

28.7 

64 

157.6 

45-2 

24 

215.3 

61.7 

84 

273.0 

78.3 

45 

43-3 

12.4 

°5 

100.  9 

28.9 

65 

158.6 

45-5 

25 

2j6.3 

62.  o 

85 

274.0 

78.6 

46 

44.2 

12.7 

06 

101.9 

29.2 

66 

159.6 

45.8 

2O 

2(7.  2 

62., 

86 

274-9 

78.8 

47 

45.2 

Ij.  0 

°7 

102.  9 

29.5 

67 

1  60.  5 

46.  o 

27 

218.2 

62.6 

87 

275-9 

79-' 

48 

46.1 

13-2 

08 

103.8 

29.8 

68 

161.5 

46-3 

28 

219.  2 

62.8 

88 

276.8 

79-4 

49 

47-' 

IJ.5 

09 

104.8 

30.  o 

69 

162.  5 

46.  6 

29 

220.  I 

63.1 

89 

277.8 

79-7 

5° 

48.1 

yj 

IO 

105.7 

3°-3 

70 

163.4 

46.9 

3° 

221.  I 

6J.4 

90 

278.8 

79-9 

5' 

49.0 

14.  i 

III 

I  ob.  7 

30.  6 

171 

164.4 

47.1 

231 

222.  I 

03.7 

291 

279-7 

80.2 

52 

50.  o 

14-  3 

12 

107.7 

3°-9 

72 

"65-3 

47-4 

32 

223.0 

63-9 

92 

280.  7 

80.5 

53 

50.9 

14.6 

13 

108.  6 

3'-i 

73 

1  66.  3 

47-7 

33 

224.  o 

64.  2 

93 

281.6 

80.8 

54 

5'-9 

14.9 

H 

109.  6 

3'-4 

74 

'67-3 

48.0 

34 

224.9 

64-5 

94 

282.6 

81.0 

55 

52.9 

15.2 

15 

no.  5 

3'-  7 

75 

168.2 

48.  2 

35 

225.9 

64.8 

95 

283.6 

8i-3 

56 

53-8 

'5-4 

16 

111.5 

32.0 

76 

169.  2 

48.5 

36 

226.  9 

6S.I 

96 

284.5 

Si.  6 

57 

54-8 

'5-7 

17 

112.5 

32.  2 

77 

170.  1 

48.8 

37 

227.8 

65.3 

97 

285.5 

Si.  9 

58 

55-8 

16.  o 

18 

II3-4 

32.5 

78 

171.1 

49.1 

38 

228.8 

65.6 

98 

286.5 

82.  i 

g 

56.7 
57-7 

16.3 
16.5 

19 
20 

114.4 
115.4 

32.8 

33-' 

79 
So 

172.1 

«73-° 

49-3 
49-6 

39 

40 

229.  7 
230.7 

65.9 

66.2 

99 
300 

287.4 
288.4 

82.4 
82.7 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[  For  74  Degrees. 

129 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  17°. 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep.    1  Dist 

Lat. 

Dep.   1  Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

I 

I.  O 

°-  3 

61 

58.3 

17.8 

121 

II5.7 

35-4 

181 

'73-1 

52.  < 

241 

230.5 

70.5 

2 

'•9 

o.  6 

62 

59-3 

18.  i 

22 

116.  7 

J5-7 

82 

174.0 

53-2 

42 

231.4 

70.8 

3 

2.9 

0.9 

63 

60.  2 

18,4 

23 

117.  6 

36.  o 

83 

175.0 

53-5 

43 

232-4 

71.0 

4 

3-1 

1.2 

64 

6l.  2 

18.7 

24 

118.  6 

35.3 

84 

176.  o 

53-8 

44 

233-3 

7L3 

5 

4.8 

«-5 

65 

62.2 

19.  o 

25 

"9-5 

36.5 

85 

176.9 

54-1 

45 

234.3 

71.6 

6 

5-7 

1.8 

66 

63.I 

19-3 

26 

120.  5 

36.8 

86 

'77-9 

54-4 

46 

235-3 

71.9 

7 

6-7 

2.  O 

67 

64.I 

19.  6 

27 

121.  S 

37-1 

87 

178.8 

54-7 

47 

236.2 

72.2 

8 

7-7 

2-3 

68 

65.  o 

19.9 

28 

122.4 

37-4 

88 

179.8 

55-0 

48 

237.2 

72.5 

9 

8.6 

2.6 

69 

66.0 

2O.  2 

29 

123-4 

37-7 

S$ 

1  80.  7 

55-3 

49 

238.  I 

72.8 

10 

9-6 

2-9 

70 

66.9 

20.  5 

3° 

124-3 

38.0 

90 

181.  7 

55-  ^ 

5° 

239-  I 

73-  I 

n 

10.5 

S-2 

71 

67.9 

20.8 

'3« 

125.3 

38-3 

191 

182.  7 

55-8 

251 

240.  o 

73-4 

12 

u.  S 

3-5 

73 

68.9 

21.  1 

S2 

126.  2 

38.6 

92 

183.6 

56.1 

52 

241.  o 

73.7 

>3 

12.4 

3-8 

73 

69.8 

21-3 

33 

127.  2 

38-9 

93 

184.  6 

56.4 

53 

241.9 

74-o 

»4 

13-4 

4-  i 

74 

70.8 

21.6 

34 

128.  I 

39-2 

94 

185-5 

56.7 

54 

242.9 

74-3 

'5 

'4-3 

4-4 

75 

7«-7 

21.9 

35 

129.  I 

39-5 

95 

186.5 

57-0 

55 

243-9 

74-6 

16 

'5-3 

4-7 

76 

72.7 

22.  2 

36 

130.  I 

39-8 

96 

187.4 

57-3 

56 

244.8 

74-  8 

'7 

16.3 

5-° 

77 

73-6. 

22.  5 

37 

131.  o 

40.  i 

97 

188.4 

57-6 

57 

245.8 

75-' 

18 

17.2 

5-3 

/8 

74-6 

22.8 

38 

132.0 

40.  3 

98 

184.  j 

57-9 

58 

246.7 

75-4 

'9 

18.  2 

S'S 

79 

75-5 

23-> 

39 

132.9 

40.  6 

99 

190.3 

58.2 

59 

247.7 

75-7 

20 

19.1 

S-8 

80 

76.5 

23-4 

40 

133-9 

40.9 

200 

>9'-3 

58.  s 

60 

248.6 

76.  o 

21 

20.  I 

6.  i 

81 

77-5 

23-7 

141 

134.8 

41.2 

201 

192.  2 

58.8 

261 

249.6 

76.3 

22 

21.  O 

6-4 

82 

78.4 

24.  o 

42 

135-8 

4"-5 

02 

193-2 

59.  i 

62 

250.6 

76.6 

23 

22.  O 

6.7 

83 

79-4 

24-3 

43 

136.8 

41-8 

°3 

'94-  i 

59-4 

63 

25'.  5 

76.9 

24 

23.0 

7.0 

84 

80.3 

24.  6 

44 

137-7 

42.  I 

04 

195.1 

59-6 

64 

252.5 

77-2 

25 

23-9 

7-3 

85 

8i-3 

24-9 

45 

I38-7 

42.4 

°5 

196.  o 

59-9 

65 

253-4 

77-5 

2O 

24.9 

7.6 

86 

82.2 

25.1 

46 

139.6 

42.7 

06 

197.0 

60.  2 

66 

254.4 

77-8 

27 

25.8 

7-9 

87 

83.2 

25.4 

47 

140.  6 

43-o 

°7 

198.  o 

60.5 

67 

255-3 

78.1 

28 

26.8 

8.2 

88 

84.2 

25.7 

48 

141.5 

43-3 

08 

198.9 

60.8 

68 

256.3 

78.4 

29 

27-7 

8'5 

89 

85.1 

26.  o 

49 

142.5 

43-6 

09 

199.9 

61.  i 

69 

257.2 

78.6 

3° 

28.7 

8.8 

90 

86.  i 

26.3 

5° 

>43-4 

43-  Q 

10 

200.  8 

61.  4 

70 

258.2 

78.9 

31 

29.  6 

9-  i 

91 

87.0 

26.6 

IS' 

144.4 

44.  i 

211 

201.8 

61.7 

271 

259.2 

79-2 

32 

30.  6 

9-4 

92 

88.0 

26.  9 

52 

145.4 

44-4 

12 

202.  7 

62.  o 

72 

200.  I 

79-5 

S3 

31-6 

9.6 

93 

88.9 

27.  2 

53 

146.3 

44-7 

'3 

203.  7 

62.3 

73 

26l.  I 

79-8 

34 

32-5 

9-9 

94 

89.9 

27.5 

54 

'47-3 

45.0 

'4 

204.  6 

62.6 

74 

262.  o 

So.  i 

35 

33-5 

10.2 

95 

90.8 

27.8 

55 

148.2 

45-3 

>5 

205.  6 

62.  9 

75 

263.  o 

80.4 

36 

34-4 

10.  5 

96 

91.8 

28.  1 

56 

149.2 

45.6 

16 

206.  6 

63.  2 

76 

263.9 

So.  7 

37 

35-4 

10.8 

97 

02.8 

28.4 

57 

150.  i 

45-9 

17 

207.5 

63.4 

77 

264.9 

81.0 

3» 

36.3 

n.  i 

98 

93-7 

28.7 

58 

151.1 

46.  2 

18 

208.5 

63-7 

78 

265.  9 

81.3 

39 

37-3 

II.  4 

99 

94-  7 

28.9 

59 

152.1 

46.5 

19 

209.4 

64.  o 

79 

266.8 

81.6 

40 

38.3 

ii.  7 

100 

95-6 

29.  2 

60 

153-0 

46.  8 

20 

210.  4 

64.3 

So 

267.8 

8).  9 

4' 

39-2 

12.  O 

101 

96.6 

29-5 

Ibi 

154.0 

47.1 

221 

211.3 

64.  6 

281 

268.  7 

82.2 

42 

40.  2 

12-3 

02 

97-5 

29.8 

62 

'54-9 

47-4 

22 

212.  3 

64.  9 

82 

269.7 

82.4 

43 

4I.I 

12.6 

°3 

98.5 

30.1 

63 

'55-9 

47-7 

23 

213-3 

65.2 

83 

270.  6 

82.7 

44 

42.  I 

12.9 

04 

99-5 

3°-4 

64 

156.8 

47-9 

24 

214.  2 

65-5 

84 

271.  6 

83.0 

45 

43-o 

13-2 

°5 

100.  4 

3°-7 

65 

157.8 

48.2 

25 

215.  2 

65.  8 

85 

272-5 

83-3 

46 

44.0 

«3-4 

06 

101.  4 

31.0 

66 

158.7 

48.5 

26 

216.  i 

66.1 

86 

273-5 

83.6 

47 

44-9 

'3-7 

07 

102.  3 

3>-3 

67 

159-7 

48.8 

27 

217.  I 

66.4 

8Z 

274-5 

83-9 

48 

45-9 

14.  o 

08 

I03-3 

3'-  6 

68 

1  60.  7 

49.1 

28 

218.0 

66.  7 

88 

275-4 

84.2 

49 

46.9 

'4-3 

09 

104.  2 

3'-9 

69 

161.6 

49-4 

29 

219.0 

67.  o 

89 

276.4 

84.S 

5° 

47-8 

14.6 

10 

105.  2 

32.2 

70 

162.6 

49-  7 

3«> 

22O.  O 

67.2 

90 

277-3 

84.8 

5' 

48.  8 

14.9 

III 

1  0&.  I 

32.5 

I?' 

>63-5 

50.  o 

231 

22O.  9 

67-5 

291 

2/8.3 

85.1 

52 

49-  7 

15.2 

12 

107.  I 

32.7 

72 

164.5 

5°-3 

32 

221.  9 

67.8 

92 

279.2 

85.4 

53 

5°-7 

'5-5 

13 

1  08.  1 

33-0 

73 

165.4 

50.  6 

33 

222.8 

68.1 

93 

280.2 

85-7 

54 

Si.6 

15.8 

14 

109.  o 

33-3 

74 

166.4 

5°-9 

34 

223".  8 

68.4 

94 

281.2 

86.0 

55 

52.6 

16.  i 

'5 

no.  o 

33-6 

75 

167.4 

5'-2 

35 

224-  7 

68.7 

95 

282.  I 

86.2 

56 

53-6 

16.  4 

16 

no.  9 

33  9 

76 

168.3 

5'-5 

36 

225.7 

69.  o 

96 

283.  i 

86.5 

57 

54-5 

16.7 

17 

111.9 

34-2 

77 

169.3 

5'-  7 

37 

226.6 

69-3 

97 

284.  o 

86.8 

58 

55-5 

17.0 

18 

112.  8 

34-5 

78 

I7O.  2 

52.0 

38 

227.  6 

69.6 

98 

2815.0 

87-1 

59 

56-4 

17.2 

19 

113.8 

34-8 

79 

171.  2 

52.3 

39. 

228.6 

69.9 

99 

285.9 

87.4 

60 

57-4 

'7-5 

20 

114.8 

35-  i 

So 

I72.I 

S2--6 

40 

229.5 

70.  2 

300 

286.9 

S7.7 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  73  Degrees. 

130 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  18°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

DUt. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dtp. 

, 

I.o 

0-3 

61 

58.0 

IS.  9 

121 

II5.I 

37-4 

181 

172.1 

55-9 

241 

229.  2 

74-5 

2 

1.9 

0.6 

62 

59-0 

19.2 

22 

1  1  6.  o 

37-7 

82 

173-1 

42 

230.2 

74-8 

3 

2.  9 

o-9 

63 

59-9 

19.5 

23 

117.0 

38.0 

83 

174.0 

56.6 

43 

231.  I 

75-1 

4 

3.8 

1.2 

64 

60.  9 

19.8 

24 

•117.9 

38.3 

84 

175-0 

56-9 

44 

232.  I 

75-4 

5 

4.8 

i.  5 

65 

61.8 

2O.  I 

25 

118.9 

38.6 

85 

175-9 

57-2 

45 

233.0 

75-7 

6 

5-7 

1.9 

66 

62.8 

20.4 

26 

119.8 

38-9 

86 

176.9 

57-5 

46 

234-0 

76.0 

7 

6-7 

2.2 

67 

63.7 

20.  7 

27 

120.8 

39-2 

87 

177.8 

57-8 

47 

234.9 

76.3 

8 

7.6 

2.5 

68 

64-7 

21.0 

28 

121.  7 

39-6 

88 

178.8 

58.1 

48 

235-9 

76.6 

9 

8.6 

2.8 

69 

65.6 

21.3 

29 

122.7 

39-9 

89 

179-7 

58.4 

49 

236.8 

76.9 

IO 

9-5 

3-  i 

70 

66.6 

21.6 

3° 

123.  6 

40.2 

90 

180.7 

58.7 

50 

237-8 

77-3 

ii 

10.5 

3-4 

7' 

67.5 

21.9 

131 

124.6 

40.  5 

191 

lSl.7 

59-0 

251 

238.7 

77-6 

12 

II.  4 

3-7 

72 

68.5 

22.  2 

32 

125.5 

40.8 

182.6 

59-3 

52 

239-7 

77-9 

13 

12.4 

4.0 

73 

69.4 

22.6 

33 

126.  5 

41.1 

93 

183.6 

59-6 

53 

240.  6 

78.2 

14 

13-3 

4-3 

74 

70.4 

22.9 

34 

127.4 

41.4 

94 

184.5 

59-9 

54 

241.  6 

78-  5 

15 

14-3 

4.6 

71-3 

23.2 

35 

128.4 

41.7 

95 

i"5-  5 

60.3 

55 

242.5 

78.8 

10 

15.  2 

4-9 

76 

72-3 

23-5 

36 

129-3 

42.  o 

96 

1  86.  4 

60.6 

56 

243-5 

79-  i 

17 

16.  2 

5-3 

77 

73-2 

23.8 

37 

130-3 

42-3 

97 

187.4 

60.  9 

57 

244.4 

79-4 

18 

I7.I 

5-6 

78 

74-2 

24.  I 

38 

131.2 

42.6 

98 

188.3 

61.2 

58 

245-4 

79-7 

"9 

18.  i 

5-9 

79 

75-1 

24.4 

39 

132.2 

43-0 

99 

189-3 

61.5 

59 

246.3 

80.0 

20 

19.  o 

6.  2 

So 

76.1 

24.7 

40 

I33.I 

43-3 

200 

190.2 

61.8 

60 

247-3 

80.3 

21 

20.  O 

75.  5 

81 

77-o 

25.  o 

MI 

I34-I 

43-6 

201 

191.  2 

62.1 

261 

248.2 

oo.  7 

22 

20.  9 

6.8 

82 

78.0 

25-3 

42 

I35-I 

43-9 

O2 

192.  I 

62.4 

62 

249.2 

81.0 

23 

21.9 

7-  1 

83 

78.9 

25.6 

43 

136.0 

44-2 

03 

193-  1 

62.7 

63 

250.  i 

8'-  3 

24 

22.8 

7-4 

84 

79-9 

26.  o 

44 

i37-o 

44-5 

04 

194.0 

63.  o 

64 

251.  i 

81.6 

25 
26 

23.8 

24.7 

7-7 
8.0 

85 
86 

80.8 
81.8 

26.3 
26.6 

45 
46 

137-9 
138.9 

44.8 
45.1 

% 

195.0 
195-9 

63-3 
63.7 

65 
66 

252.  o 
253-0 

81.9 
82.2 

11 

25.7 
26.6 

8-3 
8.7 

87 
88 

82.7 
83.7 

26.  9 
27.2 

47 
48 

139.8 
140.  8 

45-4 
45-  7 

07 
08 

196.9 
197.8 

64.  o 

64.3 

n 

253-9 
254.9 

82.5 
82.8 

29 

27.6 

9.0 

89 

84.6 

27-5 

49 

141.7 

46.  o 

09 

198.8 

64.6 

69 

255.8 

8;.  i 

30 

28.5 

9-3 

90 

8=.6 

27.8 

5o 

142.  7 

46.4 

IO 

199.  7 

64.9 

70 

256.8 

83-4 

31 

29.5 

9.6 

9' 

86.5 

28.1 

151 

143.6 

46.  7 

211 

200.  7 

65.2 

271 

257-7 

83.7 

32 

30.4 

9-9 

92 

87.5 

28.4 

144.6 

47.0 

12 

201.  6 

65.5 

72 

258.7 

84.1 

33 

31.4 

IO.  2 

93 

88.4 

28.7 

53 

'45-5 

47-3 

13 

202.  6 

65.8 

73 

259.6 

84.4 

34 

32-3 

10.  5 

94 

89-4 

29.  o 

54 

146.5 

47.6 

H 

203.5 

66.  i 

74 

260.  6 

84.7 

35 

33-3 

10.8 

95 

90.4 

29.4 

55 

147-4 

47-9 

'5 

204.5 

66.4 

75 

261.  5 

85.0 

36 

34-2 

II.  I 

96 

9'-3 

29-  7 

56 

148.4 

48.2 

16 

205.4 

66.7 

76 

262.  5 

85-3 

37 

35-2 

11.4 

97 

92.3 

30.0 

57 

149-3 

48.5 

17 

206.  4 

67.1 

77 

263.4 

85.  o 

38 

36.1 

11.7 

98 

93-2 

30-3 

58 

150.3 

48.8 

•  18 

207.3 

67.4 

?ij 

264-4 

85.9 

39 

37-1 

12.  I 

99 

94-2 

30.6 

59 

151.2 

49-  i 

19 

208.  3 

67.7 

79 

265-  3 

-86.2 

40 

38.0 

I2.4 

ioo 

95-1 

30-9 

60 

152.2 

49-4 

20 

209.  2 

68.0 

OO 

266.  3 

86.5 

41 

39-0 

12.  7 

101 

96.  i 

31.2 

161 

153-  i 

49-8 

221 

210.  2 

68.3 

281 

267.  2 

86.8 

42 

39-9 

13-0 

02 

97.0 

31-5 

62 

154.1 

50.1 

22 

211.  I 

68.  6 

82 

268.2 

87-1 

43 

40.9 

'3-3 

°3 

98.0 

31.8 

63 

155-0 

50.4 

23 

212.  I 

68.9 

83 

269.  i 

87-5 

44 

41.8 

'3-6 

04 

98.9 

32.1 

64 

156.0 

5°-7 

24 

213.  o 

69.  2 

84 

270.  i 

87.8 

45 

42.8 

13-9 

99-9 

32-4 

65 

156.9 

51.0 

25 

214.  o 

69.  5 

85 

271.1 

88.  i 

46 

43-7 

14.2 

06 

loo.S 

32-8 

66 

157-9 

51-3 

26 

214.9 

69.8 

86 

272.  o 

88.4 

47 

44-  7 

14-5 

07 

101.8 

33-i 

67 

158.8 

51.6 

27 

215.9 

70.  1 

87 

273.0 

88.7 

48 

45-7 

14.8 

08 

102.  7 

33-4 

68 

159.8 

5i-9 

28 

216.  8 

70.5 

88 

273-9 

89.0 

49 

46.6 

I5-I 

09 

103-7 

33-7 

69 

160.  7 

52.2 

29 

217.8 

70.8 

89 

274-9 

89-3 

50 

47.6 

'5-5 

10 

104.  6 

34-0 

70 

161.  7 

52-5 

3° 

218.  7 

71.1 

90 

275-8 

89.6 

51 

48.5 

15/8 

III 

105.  6 

34-3 

171 

162.  6 

52.8 

231 

219.7 

71.4 

291 

276.8 

89.9 

52 

49-5 

16.  i 

12 

1  06.  5 

34-6 

72 

163.6 

53-2 

32 

220.  6 

7'-7 

92 

277-7 

90.  2 

53 

,50.4 

16.4 

13 

107.5 

34-9 

73 

164.5 

53-5 

33 

221.6 

72.0 

93 

278.7 

90.  5 

54 

Si-4 

16.7 

14 

108.4 

35-2 

74 

165-5 

53-8 

34 

222.  5 

72.3 

94 

279.6 

90.9 

55 

52.3 

17.0 

15 

109.4 

35-5 

75 

166.4 

54-1 

35 

223.5 

72.6 

95 

280.  6 

91.2 

56 

53-3 

!7-3 

.16 

no.  3 

35-8- 

76 

167.4 

54-4 

36 

224.4 

72.9 

96 

281.  5 

91.5 

57 

54-2 

17.6 

17 

111.3 

36.  2 

77 

168.3 

54-7 

37 

225.4 

73-2 

97 

282.5 

91.8 

58 

55-2 

17-9 

18 

112.  2 

36.5 

78 

169.3 

55-o 

38 

226.  4 

73-5 

98 

283.4 

92.1 

59 

56.1 

IS.  2 

19 

113-2 

36.8 

79 

170.  2 

55-3 

39 

227-3 

73-9 

99 

284.4 

92.4 

60 

57.  i 

18.5 

20 

II4.I 

37-1 

80 

I7I.2 

55-6 

40 

228.  3 

74-2 

300 

285-3 

92.7 

Dist. 

Dcp, 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lai. 

Dist. 

Dep. 

Lat 

[For  72  Degrees. 

131 


DIFFERENCE  OF  LATITUDE 

AND  DEPARTURE  FOR  19°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lit. 

Dep. 

Dist. 

L^t. 

Dcp. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0-3 

61 

57-7 

19.9 

12! 

114-4 

39-4 

iSi 

J7LI 

58.9 

241 

227.9 

78.5 

2 

i;  9 

0.7 

62 

58.6 

2O.  2 

22 

115.4 

39-7 

82 

I72.I 

59-3 

42 

228.8 

78.8 

3 

2.8 

I.  O 

63 

59-6 

20.5 

23 

no.  3 

40.  o 

83 

173.0 

59.6 

43 

229.8 

79.1 

4 

3-8 

i.  3 

64 

60.  5 

20.8 

24 

117.2 

40.4 

84 

174.0 

59-9  . 

44 

230.  7 

79-4 

5 

4-7 

1.6 

65 

61.5 

21.2 

25 

IlS.  2 

40.  7 

85 

1  74-  9 

60.  2 

45 

231.7 

79-8 

6 

5-7 

2.0 

66 

62.4 

21.  5 

26 

119.  i 

41.  o 

86 

175-9 

60.6 

46 

232.6 

80.  i 

7 

6.6 

2.  3 

67 

63-3 

21.8 

27 

120.  I 

41-3 

87 

176.8 

60.  9 

47 

233-5 

80.4 

8 

7-6 

2.6 

68 

64.3 

22.  I 

28 

121.  O 

41.7 

88 

177-8 

61.2 

48 

234-  5 

80.7 

9 

8.5 

2-9 

69 

65.2 

22.  5 

29 

122,  O 

42.  o 

89 

178.7 

61.5 

49 

235-4 

81.  i 

10 

9-5 

3-3 

70 

66.2 

22.8 

30 

122-9 

42.3 

90 

179.6 

61.  9 

5° 

236.4 

81.4 

ii 

10.  4 

3-6 

7i 

67.  i 

23-1 

131 

123.9 

42.  6 

191 

1  80.  6 

62.  2 

251 

237.3 

81.7 

12 

"•3 

3-9 

72 

68.1 

23-4 

32 

I£4.8 

43-  ° 

92 

181.5 

62.5 

52 

238-3 

82.0 

13 

12.3 

4-2 

73 

69.  o 

23.8 

33 

25.  8 

43-3 

93 

182.5 

62.8 

53 

239.2 

82.4 

14 

'3-  2 

4.6 

74 

70.  o 

24-  I 

34 

26.  7 

43-6 

94 

183.4 

63.2 

54 

240.2 

82.7 

15 

14.2 

4-9 

75 

70.9 

24-4 

35 

27.6 

44-o 

95 

184.4 

63.5 

55 

241.  I 

83.0 

16 

15.  i 

5-2 

76 

71-9 

24-7 

28.6 

44-3 

96 

185-3 

63.8 

56 

242.  1 

83-3 

17 

16.  i 

5-5 

77 

72.8 

25-1 

37 

29-5 

44.6 

97 

186.3 

64.1 

57 

243.0 

83-7 

18 

17.0 

5-9 

78 

73-8 

25-4 

38 

130.5 

44-9 

98 

187.2 

64.5 

58 

243.9 

84.0 

19 

18.  o 

6    2 

79 

74-7 

25-7 

39 

I3I-4 

45-3 

99 

188.2 

64.8 

59 

244.9 

84-3 

20 

18.9 

6.5 

So 

75-6 

26.  o 

40 

132-4 

45-6 

200 

189.  I 

65.  1 

60 

245.8 

84.  6 

21 

19.9 

6.8 

81 

76.6 

26.4 

141 

133-3 

45-9 

20  L 

190.  o 

65.4 

261 

246.8 

85.0 

22 
23 

20.8 

an.  7 

7-2 

7-5 

82 
83 

77-5 
78.5 

26.7 

27.  o 

42 
43 

134.3 
135-2 

46.2 
46.6 

O2 

191.  o 

191.9 

65.8 

66.  I 

62 
63 

247.7 
248.7 

85-3 
85.6 

24 

22.  7 

7-8 

84 

79-4 

27.3 

44 

136.  2 

46.9 

04 

192.9 

66.4 

64 

249.6 

S6.o 

25 

23.  6 

8.1 

85 

80.4 

27.7 

45 

I37-I 

47-2 

05 

193.8 

66.  7 

65 

250.  6 

86.3 

26 

24.  6 

8-  5 

86 

Si.  3 

28.0 

46 

138.0 

47-5 

06 

194.8 

67.1 

66 

2.5  '-5 

86.6 

27 

25-5 

8.8 

8? 

82.3 

28.3 

47 

139-0 

47-9 

07 

195.7 

67-4 

67 

252-5 

86.9 

28 

26.5 

9-  i 

88 

83.2 

28.7 

48 

139-9 

48.2 

08 

196.7 

67-7 

68 

253-4 

87-3 

29 
30 

27-4 
28.4 

9-4 
9-8 

89 
90 

84.2 
85.1 

29.  o 

29.3 

49 
5° 

140.  9 
141.8 

48.5 
48.8 

09 

io 

197.6 
198.6 

68.0 
68.4 

69 
70 

254-3 
255-3 

87.6 
87.9 

31 

29-3 

10.  I 

91 

86.0 

29.  6 

151 

142.8 

49-2 

211 

199.5 

68.7 

271 

256.2 

SS.  2 

32 

30-3 

10.4 

92 

87.0 

30.  o 

52 

143-7 

49-5 

12 

200.  4 

69.  o 

72 

257-2 

88.6 

33 

31-2 

10.7 

93 

87.9 

30.3 

53 

144-  7 

49-8 

13 

201.  4 

69.3 

73 

258.  i 

88.9 

34 

32-1 

II.  I 

94 

88.9 

30.6 

54 

145.6 

50.1 

14 

202.  3 

69.7 

74 

259.  i 

89:2 

35 

33-1 

II.  4 

95 

89.8 

30.9 

55 

146.  6 

5°-5 

15 

203.3 

70.  o 

75 

260.  o 

S9-5 

36 

34-0 

"•  7 

96 

90.8 

3'-3 

56 

147-5 

50.8 

16 

204.  2 

70.3 

76 

261.  o 

89.9 

37 

35-0 

12.  0 

97 

91-7 

31.6 

57 

148.4 

5'-  1 

17 

205.  2 

70.6 

77 

261.  9 

90.  2 

38 

35-9 

12.4 

08 

92-7 

31-9 

58 

149.4 

51-4 

18 

2OO.  I 

71.0 

78 

262.  9 

90.5 

39 

36-  9 

12.7 

99 

93-6 

32.2 

59 

I50-3 

51.8 

19 

207.  I 

71-3 

79 

263.8 

90.  8 

40 

37-8 

I3.0 

100 

94-6 

32.6 

60 

I5I-3 

52.1 

20 

208.  o 

71.6 

80 

264.7 

91.2 

4i 

38.8 

13-3 

101 

95-5' 

32.9 

161 

152.  2 

52-4 

221 

209.  o 

72.0 

281 

265.7 

91.5 

42 

39-  7 

13-7 

02 

96.4 

33-2 

62 

153-2 

52.7 

22 

209.9 

72-3 

82 

266.  6 

91.8 

43 

40.  7 

M.O 

°3 

97-4 

33-5 

63 

I54.I 

53-i 

23 

210.  9 

72.  6 

83 

267.6 

92.1 

44 

41.  6 

14-3 

04 

98.3 

33-9 

64 

I55-I 

53-4 

24 

211.  8 

72.9 

84 

268.5 

92.5 

45 

42.5 

14-7 

05 

99-3 

34-2 

65 

156.  o 

53-7 

25 

212.7 

73.3 

85 

269.5 

92.8 

46 

43-5 

15.0 

06 

100.  2 

34-5 

66 

157.0 

54.0 

26 

213.7 

73-6 

86 

270.4 

93-1 

47 

44-4 

15-3 

07 

IOI.  2 

34-8 

67 

157-9 

54-4 

27 

214.6 

73-9 

87 

271.4 

93-4 

48 

45-4 

15.6 

oS 

102.  I 

35-2 

63 

158.8 

54-  7 

28 

215.6 

74-2 

88 

272.  3 

93-8 

49 

46.3 

16.  o 

09 

103.  I 

35-5 

69 

159.8 

55-o 

29 

216.  5 

74-6 

89 

273-3 

94-  i 

5° 

47-3 

i6-3 

10 

104.  o 

35-<* 

70 

160.  7 

55-3 

3° 

217.5 

74-9 

90 

274.2 

94-4 

51 

48.2 

16.  6 

in 

105.  6 

36.1 

171 

161.  7 

55-7 

231 

218.4 

75-2 

291 

275.1 

94-  7 

52 

49-2 

16.  9 

12 

105.9 

36.5 

72 

162.  6 

56.  o 

32 

219.4 

75-5 

92 

276.  i 

95-1 

53 

50.1 

17-3 

13 

106.8 

36.8 

73 

163.6 

56.3 

33 

220.3 

75-9 

93 

277.0 

95-4 

54 

51.1 

17-6 

14 

107.8 

37-1 

74 

iC^.  5 

56.6 

34 

2-21.3 

76.2 

94 

278.0 

95-7 

9 

52.0 
52.9 

17-9 
18.  2 

15 
l6 

icS.  7 
109.  7 

37-4 
37-8 

11 

165.5 
166.4 

57-0 
57-3 

9 

222.  2 
223.1 

76.5 
76.8 

95 
96 

278.9 
279.9 

96.  o 
96.4 

57 

53-9 

18.  6 

17 

no.  6 

38-1 

77 

167.4 

57-6 

37 

224.  1 

77-2 

97 

280.8 

96.7 

58 

54-8 

18.9 

18 

in.  6 

38.4 

78 

168.3 

5-o 

38 

225.  o 

77-5 

98 

281.8 

97.0 

59 

60 

55.8 
56.7 

19.  2 

19.5 

19 

20 

112.5 
II3-5 

38.7 
39-1 

79 

80 

169.  2 
170.  2 

58.3 
58.6 

39 

40 

226.  o 
226.  9 

n-8 

78-1 

99 
300 

282.  7 
283.7 

97-3 
97-7 

Dist. 

Dcp. 

Lat. 

Dist. 

Dcp. 

Lat, 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dcp. 

Lat. 

["1'or  71  Degrees. 

132 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  20°. 

Dist. 

Lot. 

Dcp. 

Dist 

Lat. 

Dcp. 

Dist. 

Lat. 

Dcp. 

Dist. 

I.at 

Dep. 

Dlst. 

L& 

0^,. 

I 

0.9 

°-3 

61 

57-3 

20.  9 

121 

"3-7 

41.4 

181 

170.  I 

6l.  9 

241 

226.  5 

82.4 

2 

1.9 

o.  7 

62 

5S-3 

21.  2 

23 

114.6 

41.7 

82 

171.0 

62.2 

42 

227.4 

82.8 

3 

2.8 

I.O 

63 

59-2 

21.5 

23 

115.  6 

42.  I 

83 

1/2.  O 

62.6 

43 

228.3 

83.1 

4 

3-8 

1.4 

64 

bo.  i 

21.9 

24 

lift.  S 

42.4 

84 

172.9 

62.  9 

44 

229.3 

83-5 

5 

4-  7 

'•  7 

65 

61.  I 

22.  2 

25 

117.5 

42.8 

»5 

173-8 

63-3 

45 

2jO.  2 

83.  S 

6 

5.6 

2.  I 

66 

62.  o 

22.6 

26 

118.4 

43-  I 

86 

174-8 

63.6 

46 

231.2 

84.  1 

7 

6.6 

2.4 

67 

63.  o 

22.9 

27 

"9.3 

43-4 

87 

J75-  7 

64.  o 

47 

232.  I 

84.5 

8 

7-5 

2-7 

68 

63.9 

23-3 

28 

120.  3 

43-8 

88 

176.7 

64-3 

48 

233.0 

84.  S 

9 

8-5 

3-J 

69 

64.8 

23.6 

29 

121.  2 

44-  > 

89 

177.6 

64.6 

49 

234.0 

85.2 

10 

9-4 

3-4 

70 

65.8 

23.9 

30 

122.  2 

44-5 

90 

178.5 

65.  o 

50 

234.9 

85-5 

11 

10.3 

3-« 

7> 

66.  7 

24.3 

I3« 

I23-I 

44-8 

191 

179.5 

65.3 

251 

235.9 

85.8 

12 

"•3 

4-  I 

72 

67.7 

24-6 

32 

124.  o 

45-  ' 

92 

180.4 

65.7 

52 

236.  8 

86.2 

13 

12.2 

4-4 

73 

68.6 

25.0 

33 

125.  o 

45-5 

93 

181.4 

66.0 

53 

237-7 

86.5 

M 

'3-2 

4.8 

74 

69.5 

25-3 

34 

125.9 

45-8 

94 

182.3 

66.4 

54 

238-7 

86.9 

IS 

I4.I 

5-' 

75 

70-5 

25.7 

35 

126.  9 

46.  2 

95 

183.2 

66.  7 

55 

239.6 

87.2 

10 

15.0 

5-5 

76 

71.4 

26.  o 

36 

127.8 

46.5 

96 

184.2 

67.0 

5° 

240.  6 

87.6 

'7 

16.  o 

77 

72-4 

26.3 

37 

128.  7 

46.9 

97 

185.  i 

67.4 

57 

241.5 

87.9 

18 

16.  9 

6.  2 

78 

73-3 

26.7 

38 

129.  7 

47-2 

98 

186.1 

67.7 

ss 

242.4 

bS.  2 

19 

17-9 

6.5 

79 

74.2 

27.  o 

39 

130.  6 

47-5 

99 

187.0 

68.  i 

59 

243-4 

88.6 

20 

18.  8 

6.8 

80 

75-2 

27.4 

40 

131.  6 

47-9 

200 

187.9 

68.4 

60 

244-3 

88.9 

21 

19.7 

7-2 

Si 

76.1 

27.7 

141 

132.5 

4S.2 

2OI 

188.9 

r68.  7 

261 

245-3 

89-3 

22 

20.  7 

7-5 

82 

77-1 

28.0 

42 

133-4 

48.6 

O2 

189.8 

69.1 

62 

246.2 

89.6 

23 

21.  6 

7-9 

«3 

•78.0 

28.4 

43 

>34-  4 

48.9 

°3 

190.8 

69.4 

63 

247.  l 

90.0 

24 

22.  6 

8.2 

84 

/8.9 

28.7 

44 

'35-3 

49-3 

04 

191.7 

69.8 

64 

248.  I 

90-3 

25 

23-5 

8.6 

85 

79-9 

29.  I 

45 

«36.3 

49.6 

05 

192.  6 

70.1 

65 

249.0 

90.  6 

26 

24.4 

8.9 

86 

80.8 

29.4 

46 

137-2 

49-9 

06 

193-6 

70.5 

66 

250.  o 

91.0 

27 

25.4 

9.2 

87 

81.8 

29.  8 

47 

138.1 

5°-3 

07 

'94-5 

70.8 

67 

250.9 

91-3 

28 

26.3 

9-6 

88 

82.7 

30.1 

48 

139.  I 

50.  6 

08 

•95-5 

71.1 

.68 

251.8 

9«-7 

29 

27-3 

9-9 

89 

83.6 

3°-4 

49 

140.  o 

51.0 

09 

196.4 

71-5 

69 

252.8 

92.0 

3° 

28.2 

10.3 

90 

84.6 

30.8 

5° 

140.  o 

5'-3 

IO 

197-3 

71.8 

70 

253-7 

92.3 

3' 

29.  I 

10.6 

9« 

85.5 

3'-  ' 

'5' 

141.9 

51.6 

211 

"98.3 

72.2 

271 

254-7 

92.7 

32 

3°-l 

10.  9 

92 

86.5 

3'-  5 

52 

142.8 

52.0 

I? 

199.2 

72.5 

72 

255-6 

93-  ° 

33 

31.0 

"•3 

93 

87.4 

3«-8 

53 

143.8 

52-3 

'3 

200.  2 

72.9 

73 

256.5 

93-4 

34 

3'-9 

11.6 

94 

88.3 

32.1 

54 

144-7 

52-7 

14 

201.  I 

73-2 

74 

257-5 

93-7 

35 

32.9 

12.  O 

95 

89.3 

32.5 

55 

"45-7 

53.0 

15 

202.  O 

73-5 

75 

258.4 

94-  « 

36 

33-8 

I2.3 

96 

90.  2 

32.8 

56 

146.6 

53-4 

16 

203.0 

73-9 

70 

259.4 

94-4 

37 

34-8 

12.7 

97 

91.2 

33-2 

57 

147-5 

53-7 

>7 

203.9 

74-2 

77 

260.  3 

94-  / 

3» 

35-7 

13-0 

98 

92.1 

33-5 

58 

148.5 

54-0 

18 

204.9 

74.6 

78 

26l.  2 

95.  I 

39 

36.6 

'3-3 

99 

93-  ° 

33-9 

59 

149.4 

54-4 

"9 

205.8 

74-9 

79 

262.  2 

95-4 

40 

37-6 

>3-7 

100 

94.0 

34-2 

60 

150.4 

54-7 

20 

206.  7 

75-2 

So 

263.  1 

95-8 

4' 

3S.5 

14.  o 

101 

94-9 

34-5 

161 

>5'-3 

55-  i 

221 

207.7 

75-  0 

281 

264.  I 

96.  i 

42 

39-5 

14.4 

02 

95-8 

34-9 

62 

152.  2 

55-4 

22 

208.6 

75-9 

82 

265.0 

96.  ^ 

43 

40.4 

'4-7 

03 

96.8 

35-2 

63 

>53-2 

55-7 

23 

209.  6 

83 

265.  9 

96.8 

44 

41-3 

'5-o 

04 

97-7 

35-6 

64 

154.1 

56.1 

24 

210.  5 

76!  6 

84 

266.  9 

97-  ' 

45 

42-3 

15.4 

05 

98.7 

35-9 

65 

'55-° 

56.4 

25 

211.4 

77.0 

85 

267.8 

97  5 

46 

43-2 

'5-7 

06 

99.6 

36.3 

66 

156.0 

56.8 

26 

212.4 

77-3 

86 

268.8 

97-8 

47 

44.2 

76.  i 

07 

100.  5 

36.6 

67 

156.9 

57-  ' 

27 

213-3 

77-6 

87 

269.7 

98.  2 

48 

45.1 

16.  4 

08 

101.5 

36.9 

68 

'57-9 

57-5 

28 

214.  2 

78.0 

88 

270.  6 

98.5 

49 

46.  o 

16.  8 

09 

102.4 

37-3 

69 

158.8 

57.8 

29 

215.  2 

78.3 

89 

271.6 

98.8 

5° 

47.0 

17.1 

10 

'°3-4 

37-6 

70 

'59-  7 

58.1 

3° 

2l6.  1 

78.7 

90 

272.5 

99.  J 

5i 

47-9 

17-4 

III 

104-3 

3^-0 

171 

1  60.  7 

58.  c 

23' 

217.  I 

79.0 

291 

273-5 

99-  5 

52 

48.9 

17-8 

12 

105.  2 

38.3 

72 

161.6 

58.8 

32 

218.0 

79-3 

92 

274-4 

99-9 

53 
54 

49.8 
50.7 

18.  i 
18.5 

'3 

14 

106.  2 
107.  I 

38.6 
39-0 

73 
74 

162.6 
163-5 

59-2 
59-5 

33 
34 

218.9 
219.9 

80.0 

93 
94 

275-3 
276.  3 

100  .'. 

too.  (> 

55 

5'-7 

18.  8 

15 

108.  i 

39-3 

75 

164.4 

59-9 

35 

220.  8 

80.  4 

95 

277-2 

loo.  9 

56 

52.6 

19.2 

16 

109.  o 

39-7 

76 

'65.4 

60.  2 

36 

231.8 

80.  7 

96 

278.  i 

101.  2 

57, 

53-6 

•9-5 

'7 

109.9 

40.  o 

77 

166.3 

60.  5 

37 

222.7 

81.  i 

97 

279-  i 

101.  6 

5$ 

54-5 

19.8 

18 

110.  9 

^0.4 

78 

167-3 

60.  9 

38 

223.6 

81.4 

98 

280.  o 

101.  9 

59 

55-4 

20.  2 

19 

in.  8 

40.  7 

79 

168.2 

61.2 

39 

224.  6 

81.7 

99 

281.0 

102-  3 

60 

56.4 

20.  5 

20 

112.8 

41.  o 

80 

169.  i 

61.6 

40 

225-5 

82.1 

300 

281.9 

102.  6 

Dlst. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep, 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  70  Degrees. 

133 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  21°. 

Dist 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dop 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

I 

0.9 

0.4 

61 

56.9 

21.9 

121 

113.  o 

43  4 

IS! 

169.0 

04.9 

241 

225.0 

86.4 

2 

1-9 

0.7 

62 

57-9 

22.  2 

22 

n3-9 

43-7 

82 

169.9 

65.2 

42 

225.9 

86.7 

3 

2.8 

I.  I 

63 

58.8 

22.6 

23 

114.8 

44-1 

83 

170.8 

65.6 

43 

226.  9 

87.1 

4 

3-7 

1.4 

64 

59-7 

22.  9 

24 

115.8 

44-4 

84 

171.8 

65.9 

44 

227.8 

87.4 

5 

4-7 

1.8 

65 

60.  7 

23-3 

25 

116.  7 

44.8 

85 

172.7 

66.3 

45 

228.7 

87.8 

6 

5-6 

2.  2 

66 

61.6 

23-7 

26 

117.  6 

45.2 

86 

'73-6 

66.  7 

46 

229.  7 

83.  2 

7 

6-5 

2-5 

67 

62.3 

24-0 

27 

118,  6 

45-5 

87 

174.6 

67.  o 

47 

230.  6 

88.5 

8 

Z;5 

2.9 

68 

6.3-5 

24.4 

28 

119.5 

45-9 

88 

'75-5 

67.4 

48 

23I-5 

8S.  9 

9 

8.4 

S-2 

69 

64.4 

24.7 

29 

120.  4 

46.  2 

89 

176.4 

67-7 

49 

232.5 

89.2 

10 

9-3 

3-6 

70 

65-4 

25.1 

3° 

121.4 

46.6 

90 

1/7-4 

68.  i 

5° 

233-4 

89.6 

II 

10.3 

3-9 

71 

66.3 

25-4 

13' 

122.  3 

46.9 

191 

178.3 

68.4 

251 

234-3 

90.  o 

12 

II.  2 

4-3 

72 

67.2 

25.8 

32 

123.2 

47-3 

92 

179.2 

68.8 

52 

235-3 

9°-3 

13 

12.  I 

4-7 

73 

68.  2 

26.  2 

33 

124.  2 

47-7 

93 

180.2 

69.2 

53 

236.2 

90.  7 

14 

I3-I 

5-° 

74 

69.  i 

26.5 

34 

I2S.I 

48.0 

94 

181.  i 

69-5 

54 

237-  ' 

91.0 

15 

14.0 

5-4 

75 

70.  o 

26.  9 

35 

126.  o 

48.4 

95 

182.0 

69.9 

55 

238.1 

91.4 

16 

14.9 

5-7 

76 

71.0 

27.2 

36 

127.0 

48.7 

96 

183.0 

70.2 

56 

239.0 

91.7 

'Z 

15.9 

6.1 

77 

71.9 

27.6 

37 

127.9 

49-  l 

97 

183-9 

70.  6 

57 

239.9 

92.1 

18 

16.8 

6-5 

78 

72-8 

28.0 

38 

128.8 

49-  5 

98 

184.8 

71.0 

58 

240.9 

92.5 

19 

'7-7 

6.8 

79 

73-8 

28.3 

39 

129.8 

40.  8 

99 

185.8 

"1-3 

59 

241.8 

92.8 

20 

18.7 

7-2 

80 

74-7 

28.7 

40 

130.  7 

50.2 

200 

186.  7 

71.7 

60 

242.  7 

93-2 

21 

19.  6 

7-5 

81 

75.6 

29.0 

141 

131.  6 

50.5 

201 

187.6 

72.0 

261 

243-  7 

93-5 

22 

20.  5 

7-9 

82 

76.  6 

29.4 

42 

132.6 

50.9 

02 

188.  6 

72.4 

62 

244.6 

93-9 

23 

21.5 

8.2 

83 

77-5 

29.7 

43 

133-5 

51.2 

°3 

189.5 

72.7 

63 

245-5 

94-3 

24 

22.4 

8.6 

84 

78.4 

30.1 

44 

>34-4 

51.6 

04 

190.5 

73-1 

64 

246.5 

94-6 

25 

23-3 

9.0 

85 

79-4 

3°-5 

45 

135-4 

52.0 

°5 

191.4 

73-5 

65 

247-4 

95-o 

2O 

24-3 

9-3 

86 

So.  3 

30.8 

46 

'36-3 

52.3 

06 

192.3 

73-8 

66 

248.3 

95-3 

27 

25.2 

9-7 

87 

81.2 

31.2 

47 

'37-2 

52.7 

o? 

193-3 

74-2 

67 

249-3 

95-7 

28 

26.  i 

10.  O 

88 

82.2 

3'-5 

48 

138.2 

53-0 

08 

194.2 

74-5 

68 

250.2 

96.  o 

29 

27.1 

10.4 

89 

83.1 

3'-9 

49 

139.  i 

53-4 

09 

195.  I 

74-9 

69 

251.1 

96.4 

3° 

28.0 

10.8 

90 

84.0 

32-3 

5° 

140.  o 

53-8 

10 

196.  i 

75-3 

70 

252.1 

96.8 

3' 

28.9 

11.  i 

.91 

85.0 

32.6 

'5' 

141.0 

54.1 

211 

197.0 

75-6 

271 

253.0 

97-1 

32 

29.9 

u.  5 

9.2 

85.9 

33-  o 

52 

141.9 

54-5 

12 

197-9 

76.  o 

72 

253-9 

97-5 

33 

30.8 

11.  8 

93 

86.8 

33-3 

53 

142.8 

54-8 

13 

198.9 

76.3 

73 

254-9 

97-8 

34 

3'-7 

12.2 

94 

87.8 

33-7 

54 

"43-8 

55-2 

H 

199-8 

76.7 

74 

255-8 

98.2 

35 

32-7 

12.5 

95 

88.7 

34-0 

55 

144-7 

55-5 

15 

200.  7 

77.0 

75 

256.7 

98.6 

36 

33-6 

12.9 

96 

89.6 

34-4 

56 

145.6 

55-9 

16 

201.  7 

77-4 

76 

257-7 

98.9 

37 

34-5 

13-3 

97 

90.6 

34-8 

57 

146.  6 

56.3 

17 

202.  6 

77.8 

77 

258.6 

99-3 

38 

35-5 

I3.6 

98 

91.5 

35-1 

58 

147-5 

56.6 

18 

203.5 

78.1 

78 

259-5 

99.6 

39 

36-4 

14.0 

99 

92.4 

35-5 

59 

148.4 

57.0 

>9 

204,5 

78.5 

79 

260.5 

IOO.  O 

40 

37-3 

14-3 

IOO 

93-4 

35-  8 

60 

149.4 

57-3 

20 

205.4 

78.8 

80 

261.  4 

loo.  3 

4' 

3*3 

14.7 

101 

94-3 

36.2 

161 

'5°-3 

57-7 

221 

206.  3 

79.2 

281 

262.  3 

loo.  7 

42 

39-2 

IS.I 

02 

95-2 

36.6 

62 

151.  2 

58.1 

22 

207.3 

79-6 

82 

263.3 

101.  I 

43 

40.1 

15.4 

03 

96.2 

36-9 

63 

152.2 

58.4 

23 

208.  2 

79-9 

83 

264.  2 

101.4 

44 

41.1 

I5.8 

04 

97.1 

37-3 

64 

I53-I 

58.8 

24 

209.  1 

80.3 

84 

265.  I 

101.8 

45 

42.  o 

16.  i 

°5 

98.0 

37-6 

65 

154.0 

59-1 

25 

210.  I 

80.6 

85 

266.  I 

102.  I 

46 

42.9 

16.5 

06 

99.0 

38.0 

66 

155-0 

59-5 

26 

211.  O 

81.0 

86 

267.  o 

102.  5 

g 

43-9 
44-8 

16.8 
17.2 

°7 
08 

99-9 
100.8 

38.3 
38.7 

% 

155-9 
156.8 

59-8 

60.  2 

11 

2II.9 
212.9 

81.3 
81.7 

87 

88 

267.  9 
268.9 

102.9 
103.2 

49 

45-7 

17.6 

09 

101.8 

39-1 

69 

157.8 

60.6 

29 

213.8 

82.1 

89 

269.8 

103.  6 

5° 

46.7 

>7-9 

10 

102.  7 

39-4 

70 

158.7 

60.  9 

3° 

214.7 

82.4 

90 

270.  7 

103.9 

5' 

47.6 

i».  3 

MV 

103.  6 

39-8 

i/i 

159.  6 

61.3 

231 

215.7 

82.8 

291 

271.  7 

104.3 

52 

48.5 

18.  6 

12 

104.  6 

40.  I 

72 

160.6 

61.6 

32 

216.6 

83.1 

92 

272.  6 

104.  6 

53 

49-5 

19.0 

»3 

>°5-5 

40.5 

73 

161.  5 

62.0 

33 

217-5 

83-5 

93 

273-5 

105.  o 

54 

5°-4 

19.4 

H 

106.  4 

40.9 

74 

162.4 

62.  4 

34 

218.5 

83-9 

94 

274-5 

105.4 

55 

5i-3 

19.7 

15 

107.4 

41.2 

75 

163.4 

62.7 

35 

219.4 

84.2 

95 

275-4 

105.7 

56 

52-3 

20.  i 

16 

108.3 

41.  6 

76 

164.3 

63.1 

36 

220.  3 

84.6 

56 

276-3 

1  06.  i 

57 

53-2 

20.4 

17 

log.  2 

41.9 

n 

165.2 

63-4 

37 

221.  3 

84.9 

92 

277-3 

106.4 

58 

54.1 

20.8 

18 

110.  2 

42.3 

78 

166.2 

63.8 

38 

222.  2 

85-3 

98 

278.2 

106.  8 

So 

55-1 
56.0 

21.  I 
2I.S 

19 

20 

III.  I 
112.  0 

42.6 
43-° 

79 
So 

167.  i 
168.  o 

64.  I 
64.5 

39 

40 

223.  I 
224.  I 

85.6 
86.0 

99 
300 

279.  i 
280.1 

107.2 
107.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep, 

Lat 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

[For  69  Degrees. 

13-i 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  22°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dcp. 

n:st. 

Lat. 

Dcp. 

Dist. 

Laf. 

Dcp. 

Dist. 

Lat 

Dep. 

I 

0.9 

0.4 

6l 

56.6 

22.9 

121 

112.  2 

45-3 

181 

167.8 

67.8 

241 

223.5 

90.3 

2 

1.9 

0.7 

62 

57-5 

23.2 

22 

H3-« 

45-7 

82 

I6S.  7 

68.2 

42 

224.4 

90.7 

3 

2.8 

I.  I 

63 

58.4 

23.6 

23 

114.  o 

46.1 

83 

169.  7 

63.  6 

43 

225-  3 

9I.O 

4 

3-  7 

••5 

64 

59-3 

24.  o 

24 

115.  o 

46.5 

84 

170.  6 

68.9 

44 

226.  2 

91.4 

4-6 
5-6 

1-9 

2.  2 

U 

60.  3 
61.2 

24-3 

24.  7 

3 

115.9 

116.  8 

46.  8 
47-2 

85 

86 

171.5 
172.5 

69-  3 
69.7 

4l 
46 

227.2 
228.  I 

91.8 
92.  2 

7 

6.5 

2.6 

67 

62.1 

25.1 

27 

117.8 

47.6 

87 

173-4 

70.  i 

47 

229.  o 

92.  5 

8 

7-4 

3-° 

68 

63.  o 

25-5 

28 

118.  7 

47-9 

88 

174-3 

70.4 

48 

229.9 

92.9 

9 

8-3 

3-4 

69 

64.  o 

25.8 

29 

119.  6 

48.3 

89 

175-2 

70.8 

49 

230.9 

93-3 

10 

9-3 

3-7 

70 

64.9 

26.2 

3° 

120.  5 

48.7 

90 

176.  2 

71.2 

5° 

2JI.8 

93-7 

II 

IO.  2 

4-  i 

7i 

65.8 

26.6 

«3i 

121.  5 

49.  I 

191 

I77-I 

71-5 

251 

232.7 

94-0 

12 

II.  I 

4-5 

72 

66.8 

27.0 

32 

122.4 

49-4 

92 

178.0 

71-9 

52 

233-7 

94-4 

13 

12.  I 

4-9 

73 

67.7 

27-3 

33 

I23-3 

49.8 

93 

178.9 

72-3 

53 

234-6 

94-8 

M 

'3-° 

5.2 

74 

68.6 

27-7 

34 

124.  2 

50.2 

94 

179-9 

72.7 

54 

235-5 

95.2 

15 

'3-9 

5-6 

75 

69.5 

28.1 

35 

125.2 

50.  6 

95 

l8o.8 

73-0 

55 

236.4 

95-5 

10 

14.8 

6.0 

76 

70.5 

28.5 

3° 

I2b.  I 

50.9 

96 

181.  7 

73-4 

56 

237.4 

95-9 

17 

15.8 

6.4 

77 

71.4 

28.8 

37 

127.  o 

5i-3 

97 

182.  7 

73-8 

57 

238.3 

96.3 

18 

16.7 

6.7 

78 

72.3 

29.  2 

38 

128.0 

r«-7 

98 

183.6 

74-2 

58 

239.2 

96.6 

19 

17.6 

7-' 

79 

73-2 

29.  6 

39 

128.9 

52.1 

99 

184.5 

74-5 

59 

240.  I 

97.0 

20 

18.  s 

7-5 

80 

74-2 

30.  o 

40 

129.8 

5--  4 

200 

185.4 

74-9 

60 

241.  I 

97-4 

21 

19-5 

7-9 

Si 

75-  « 

3°-3 

141 

130.7 

52.8 

301 

ibt>.  4 

75-3 

261 

242.  o 

97-8 

22 

20.  4 

8.2 

82 

76.0 

3°-  7 

42 

131-7 

53-2 

02 

187-3 

75-7 

62 

242.9 

98.1 

23 

21.3 

8.6 

83 

77.0 

3'-' 

43 

132.6 

53-6 

°3 

ISS.  2 

76.0 

63 

243.8 

98.5 

24 

22.3 

9.0 

84 

77-9 

31-5 

44 

133-5 

53-9 

04 

189.  i 

76.4 

64 

244.8 

98.9 

25 

23.  2 

9-4 

85 

78.8 

45 

134-4 

54-3 

«>5 

190.  i 

76.8 

65 

245.7 

99-3 

26 

24.1 

9-7 

86 

79-  7 

32-2 

46 

135-4 

54-7 

06 

191.  o 

77-2 

66 

246.  6 

99-6 

27 

25.  o 

10.  I 

»7 

80.  7 

32-6 

47 

136-3 

55-1 

°7 

191-9 

77-5 

67 

247.6 

IOO.  O 

28 

26.  o 

10.5 

88 

81.6 

33-o 

48 

«37-2 

55-4 

08 

192.9 

77-9 

68 

248.5 

loo.  4 

29 

26.9 

10.  9 

89 

82.5 

33-3 

49 

138.2 

55-8 

09 

193-8 

78.3 

6» 

249.4 

100.8 

3° 

27.8 

II.  2 

90 

83.4 

33-7 

5° 

I39.I 

56.2 

10 

194.  7 

78-7 

7o 

250-3 

101.   I 

3' 

28.7 

ii.  6 

91 

84.4 

34-  i 

J5' 

140.  o 

56.  6 

211 

195.6 

79-o 

271 

251-3 

101.  5 

32 

29  7 

12.  O 

92 

&3 

34-5 

52 

140.9 

56-9 

12 

196.  6 

79-4 

72 

252.  2 

101.  9 

33 

30.  6 

12.4 

93 

86.2 

34-8 

53 

141.9 

57-3 

13 

197-5 

79.8 

73 

253.I 

102.  I 

34 

3'-  5 

12.7 

94 

87.2 

35-2 

54 

142.8 

57-7 

14 

198.4 

80.2 

74 

254.0 

102.  6 

35 

32-5 

I3-I 

95 

88.  i 

35-6 

55 

143-7 

58.1 

15 

199.3 

So.  5 

75 

255.0 

103.  o 

36 

33-4 

13-5 

96 

89.0 

36.  o 

56 

144.6 

<S.  4 

16 

200.3 

80.9 

76 

255-9 

103.4 

37 

34-3 

13-9 

97 

89.9 

36.3 

57 

145.6 

58.8 

17 

201.  2 

8'-  3 

77 

256.  8 

103.8 

38 

35-2 

14.2 

98 

90.  9 

36.7 

58 

146.5 

59.2 

18 

202.  I 

81.7 

73 

257-8 

104.  1 

39 

36.2 

14.  6 

99 

91.8 

37-  1 

59 

147-4 

59-6 

19 

203.  I 

82.0 

79 

258.7 

104.5 

40 

37-1 

15.0 

IOO 

92.7 

37-5 

60 

H8.3 

59-9 

20 

204.  o 

82.4 

80 

259.6 

104.9 

4' 

38.0 

15.4 

101 

93-  6 

37-  « 

101 

149-3 

60.  3 

221 

204.  9 

82.8 

281 

260.  5 

I05-3 

42 

38.9 

'5-7 

02 

94.6 

38.2 

62 

150.2 

60.7 

22 

205.  8 

83.2 

82 

261.  5 

105.6 

43 

39-9 

16.  i 

03 

95-5 

38.6 

63 

151.1 

61.  I 

23 

206.  8 

83.5 

83 

262.  4 

106.  o 

44 

40.8 

16.5 

04 

96.4 

39-0 

64 

152.1 

61.4 

24 

207.7 

83-9 

84 

263.3 

1  06.  4 

45 

41.7 

16.  9 

°5 

97-4 

39-3 

65 

I53.o 

61.8 

25 

208.6 

£4.3 

85 

264.2 

106.  8 

46 

42.7 

17.2 

06 

98.3 

39-7 

66 

I53.9 

62.2 

26 

209.5 

84-7 

86 

265.  2 

107.  i 

47 

43-6 

17.6 

07 

99-2 

40.  i 

67 

154.8 

62.6 

2? 

210.  5 

85.0 

87 

266.  i 

107.5 

48 

44-5 

18.  o 

08 

IOO.  I 

40.5 

68 

155.8 

62.  9 

28 

2II.4 

85.4 

88 

267.  o 

107.9 

49 

45-4 

18.4 

09 

101.  I 

40.  8 

69 

156.  7 

63-3 

29 

212.3 

85.8 

89 

268.  o 

108.3 

5° 

46.4 

18.7 

10 

IO2.  O 

41.2 

70 

157.6 

63.7 

3° 

213-3 

86.2 

90 

268.  9 

108.  6 

5' 

47-3 

19.1 

III 

102.  9 

41.  6 

171 

158.5 

64.1 

23' 

214.  2 

867s 

291 

269.  8 

109.  o 

52 

48.2 

19.5 

12 

103.8 

42.  o 

72 

159.5 

64.4 

32 

215.  I 

86.  9 

92 

270.7 

109.4 

53 

49-  I 

19.9 

«3 

104.  8 

42.3 

73 

1  60.  4 

64.8 

33 

216.  o 

87.3 

93 

271.7 

109.8 

54 

50.1 

20.2 

H 

105.7 

42.7 

74 

ifai.  3 

65.  2 

34 

217.  o 

87.7 

94 

272.  6 

I  10.  I 

55 

51.0 

20.6 

»S 

106.  6 

43-1 

75 

162.  3 

65.6 

35 

217.  o 

88.0 

95 

273-5 

no.  5 

56 

5'-9 

21.  O 

16 

107.  6 

43-5 

76 

163.  2 

65.9 

3" 

218.8 

88.4 

96 

274.4 

no.  9 

57 

52.8 

21.4 

ll 

108.5 

43-8 

77 

164.  i 

66.3 

37 

219.7 

88.8 

97 

275-4 

111.3 

58 

53-8 

21.7 

18 

109.4 

44-2 

78 

165.  o 

66.  7 

38 

220.  7 

89.  2 

98 

276.3 

ill.  6 

59 

54-7 

22.  I 

19 

no.  3 

44.6 

79 

1  66.  o 

67.1 

39 

221.  6 

89.5 

99 

277.2 

112.  O 

60 

55.6 

22-5 

20 

111.3 

45.0 

So 

166.  9 

67.4 

40 

222.  5 

89-9 

300 

278.2 

112.4 

Dist. 

Dcp. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat. 

Diet 

Dcp. 

Lat 

[For  6S  Degree*. 

135 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  23°. 

Dlst 

Lat 

Dep 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

I 

o.  g 

O.  i, 

61 

56.2 

23-8 

121 

in.  4 

47-3 

181 

166.6 

70.7 

241 

221.8 

94.2 

i 

1.8 

o.S 

62 

57-' 

'24.2 

22 

112.3 

47-7 

82 

167.5 

71.  I 

42 

222.8 

94.6 

• 

2.8 

1.2 

63 

58.0 

24.6 

23 

113.2 

48.1 

83 

168.5 

71-5 

43 

223.7 

94-9 

4 

3-7 

1.6 

64 

58.9 

25.0 

24 

114.  I 

48.5 

84 

169.4 

71.9 

44 

224.6 

95-3 

t 

4.6 

2.  O 

65 

50.8 

25-4 

25 

115.1 

48.8 

85 

170-3 

72.3 

45 

225.5 

95-7 

6 

5-5 

2.  : 

66 

60.8 

25.8 

26 

1  16.  o 

49-2 

86 

I7I.2 

72.7 

46 

226.4 

96.  i 

' 

6.4 

2.7 

67 

61.7 

26.2 

27 

116.  9 

49-6 

87 

172.1 

73-i 

47 

227.4 

96.5 

8 

7-4 

3-1 

68 

62.6 

26.6 

28 

117.8 

50.  o 

88 

I73-I 

73-5 

48 

228.3 

96-9 

9 

8-3 

3-5 

69 

63.5 

27.0 

29 

118.7 

5°-4 

89 

174.0 

73-8 

49 

229.  2 

97-3 

10 

9.2 

3-9 

70 

64.4 

27.4 

3° 

119.7 

50.8 

90 

174-9 

74-2 

5° 

230.  I 

97-7 

ii 

10.  I 

4-3 

71 

65.4 

27.7 

131 

120.6 

51.2 

191 

175.8 

74-6 

251 

23I.O 

98.  i 

12 

II.  0 

4-7 

72 

66.3 

28.  i 

32 

121.  5 

51.6 

92 

176.7 

75-° 

52 

232.  o 

98-5 

u 

12.  O 

5-i 

73 

67.2 

28.5 

33 

122.4 

52.  o 

93 

177-7 

75-4 

53 

232.9 

98.9 

14 

12.9 

5-5 

74 

68.  i 

28.9 

34 

123.3 

52.4 

94 

178.6 

75-8 

54 

233-8 

99.2 

15 

IJ.8 

5-9 

75 

69.  o 

29-3 

35 

'24.* 

52-7 

95 

179-5 

76.2 

55 

234-  7 

99.6 

16 

14.7 

6-3 

76 

70.  o 

29.7 

36 

125.2 

53-  ! 

96 

1  80.  4 

76.6 

56 

235-6 

IOO.  O 

17 

IS.6 

6.6 

77 

70.9 

30.1 

37 

126.  1 

53-5 

97 

181.3 

77.0 

57 

236.  6 

100.4 

IS 

16.  6 

7.0 

78 

71.8 

3°-5 

38 

127.0 

53-9 

98 

182.3 

77-4 

58 

237-5 

100.8 

»9 

'7-5 

7-4 

79 

72.7 

30.9 

39 

128.0 

54-3 

99 

183.2 

77-8 

59 

238-4 

IOI.2 

20 

18.4 

7.8 

So 

73-6 

3i-3 

40 

128.9 

54-7 

200 

184.  i 

78.1 

60 

239-3 

101.6 

21 

19-3 

8.2 

81 

74-6 

31.0 

141 

129.8 

55-' 

201 

185.0 

78.5 

261 

240.3 

102.0 

22 

20.3 

8.6 

8? 

75-5 

32.0 

42 

'3°-  7 

55-5 

O2 

185.9 

78.9 

62 

241.2 

102.4 

23 

21.2 

9.0 

f3 

76.4 

32.4 

43 

131.6 

55-9 

03 

186.9 

79-3 

63 

242.  i 

102.8 

24 

22.  I 

9-4 

84 

77-3 

32.8 

44 

132.6 

56.3 

04 

187.8 

79-7 

64 

243.0 

103.2 

25 

23.  o 

9.8 

85 

78.2 

33-2 

45 

'33-5 

56.7 

°5 

188.7 

80.  i 

65 

243-9 

103-5 

26 

23-9 

10.2 

86 

79-2 

33-6 

46 

134-4 

57.0 

06 

189.6 

80.5 

66 

244.9 

103.9 

27 

24-9 

IO.S 

87 

80.  i 

34-0 

47 

'35-3 

57-4 

07 

190.5 

80.0 

67 

245.8 

i°4-3 

28 

25.8 

10.  9 

88 

81.0 

34-4 

48 

136.  2 

57-8 

08 

191.5 

81.3 

68 

246.7 

104.7 

29 

26.  7 

"•3 

89 

Si.  9 

34-8 

49 

137-2 

58.2 

09 

192.4 

81.7 

69 

247.  6 

105.  i 

3° 

27.6 

11.  7 

90 

82.8 

35-2 

5° 

138.  I 

58.6 

IO 

J93-3 

82.1 

70 

248.5 

I05-5 

3' 

28.5 

12.  I 

9' 

83.8 

35-6 

151 

139.0 

59.0 

211 

194.2 

82.4 

271 

249-5 

105.9 

32 

29-5 

12-5 

92 

84.7 

35-9 

52 

'39-9 

59-4 

12 

195-1 

82.8 

72 

250.4 

106.  3 

33 

3°-4 

12.  9 

93 

85.6 

36.3 

53 

140.8 

59.8 

'3 

196.  i 

83-2 

73 

25L3 

106.  7 

34 

31-3 

13-3 

94 

86.5 

36.7 

54 

141.8 

60.  2 

U 

197.0 

83.6 

74 

252.  2 

107.  i 

35 

32-2 

13-7 

95 

87.4 

37-  i 

55 

142.7 

60.6 

15 

197-9 

84.0 

75 

253.  ! 

107.5 

36 

33-1 

14.1 

96 

88.4 

37-5 

56 

143-6 

61.0 

16 

198.8 

84.4 

76 

254.1 

107.8 

37 

34.1 

14.5 

97 

89-3 

37-9 

57 

144-  5 

61.3 

'7 

199-7 

84.8 

77 

255.0 

1  08.  2 

38 

35-o 

1.4-8 

9» 

90.2 

38.3 

58 

145-4 

61.7 

18 

200.  7 

85.2 

78 

255-9 

108.  6 

39 

35-9 

15.2 

99 

91.1 

38-7 

59 

146.4 

62.  i 

•9 

201.  6 

85.6 

79 

256.8 

109.  o 

40 

36.8 

i.S.6 

100 

92.1 

39-i 

60 

147-  3 

62.5 

20 

202.  5 

86.0 

80 

257-7 

109.4 

4i 

37-7 

16.  o' 

101 

93-° 

39-5 

161 

148.  2 

62.  9 

221 

203.4 

86.4 

281 

258.7 

109.  8 

42 

38.7 

16.  4 

02 

93-9 

39-9 

62 

149.  1 

63-3 

22 

204.4 

86.7 

82 

259-6 

110.  2 

43 

39-6 

16.  8 

°3 

94.8 

40.  2 

63 

150.  o 

63.7 

23 

205.3 

87., 

83 

260.  5 

no.  6 

44 

40.5 

17.2 

04 

95-7 

40.  6 

64 

151.  o 

64.1 

24 

206.  2 

87.5 

84 

261.4 

III.  0 

45 

41-4 

17.6 

°5 

96.7 

41.0 

65 

151.9 

64.5 

25 

207.  I 

87.9 

85 

262.  3 

111.4 

46 

42.3 

18.  o 

06 

97-6 

41.4 

66 

152.8 

64.9 

26 

208.  o 

88.3 

86 

263-3 

in.  7 

47 

43-3 

18.  4 

07 

98.5 

41.8 

6J- 

153-7 

65.3 

27 

209.  o 

88.7 

87 

264.2 

112.  I 

48 

44-2 

18.8 

oS 

99-4 

42.2 

68 

154.6 

65.6 

28 

209.9 

89.1 

8S 

265.  i 

112.5 

49 

45.' 

19.1 

09 

loo.  3 

42.6 

69 

MS-  6 

66.0 

29 

210.8 

89.5 

89 

266.  o 

112.  9 

5° 

46x1 

'9-5 

10 

101.  3 

43-o 

70 

I56-S 

66.4 

3° 

211.  7 

89.9 

90 

266.  9 

113.3 

5' 

46.9 

19.9 

III 

102.  2 

43-4 

171 

'57-4 

66.8 

231 

212.  6 

9°-3 

291 

267.9 

"3-7 

52 

47..9 

°-3 

12 

103.  I 

43-8 

72 

158-3 

67.  2 

32 

213.6 

go.  6 

92 

268.8 

114.  i 

53 

48.8 

o.  7 

'3 

104.0 

44-2 

73 

159.2 

67.6 

33 

214.5 

91.0 

93 

269.7 

"4-5 

54 

49-7 

i.  I 

'4 

104.9 

44.  5 

74 

1  60.  2 

68.0 

34 

215.4 

91.4 

94 

270.6 

114.9 

55 

50.  6 

'•5 

'5 

>os-  9 

44-9 

75 

161.  i 

68.4 

35 

2  1  6.  3 

91.8 

95 

271.5 

iiS-3 

56 

51-5 

1-9 

10 

1  06.  8 

45-3 

76 

162.  o 

68.8 

3S 

217.  2 

92.2 

96 

272.5 

115.7 

SZ 

5a-S 

2-3 

17 

107.7 

45-7 

77 

162.9 

69.  2 

37 

218.2 

92.6 

97 

273-4 

no.  o 

58 

53-4 

2-7 

.18 

108.  6 

46.  I 

78 

163.8 

69.6 

38 

219.  I 

93-o 

98 

274-3 

116.4 

59 

54-3 

3-  I 

«9 

i°9-5 

46.5 

79 

164.8 

69.9 

39 

220.  O 

93-4 

99 

275.2 

116.8 

60 

55-  * 

3-4 

20 

no.  5 

46.9 

86 

165.7 

70.3 

40 

220.9 

93-8 

300 

276.2 

117.2 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

L«t. 

[For  67  Degrees. 

130 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  24°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep 

I 

0.9 

0.4 

61 

55-7 

24.8 

121 

no.  5 

49-2 

181 

165.4 

73-6 

241 

220.  2 

98.  0 

2 

1.8 

0.8 

O2 

56.6 

25.2 

22 

in.  5 

49-  6 

82 

1  66.  3 

74-o 

42 

221.  I 

98.4 

3 

2-7 

I.  2 

63 

57-6 

25.  6 

23 

112.4 

50.  o 

83 

167.  2 

74-4 

43 

222.  O 

98.8 

4 

3-  7 

1.6 

64 

58.5 

26.  o 

24 

"3-3 

50.4 

84 

1  68.  I 

74-8 

44 

222.  9 

99-2 

6 

4-6 
5-  5 

2.  O 
2-4 

§ 

59-4 
60.3 

26.4 
26.8 

26 

II4-  2 
115.  I 

50.8 
51.2 

85 
86 

169.  o 
169.  9 

75-2 
75-7 

46 

223.8 

224.  7 

99-  7 

IOO.  I 

7 

6.4 

2.8 

67 

61.2 

27-3 

27 

lib.  o 

51-7 

87 

170.  8 

fg.1 

47 

225.6 

loo.  5 

8 

7-3 

3-3 

68 

62.1 

27-7 

28 

116.  9 

52.1 

88 

171.7 

76-5 

48 

226.  6 

loo.  9 

9 

8.2 

3-7 

69 

63.  o 

28.  i 

29 

117.8 

52-5 

89 

172.7 

76.9 

49 

227.5 

101.  3 

10 

9-  « 

4-1 

70 

63-  9 

28.5 

30 

118.  8 

52.9 

90 

173-6 

77-3 

50 

228.4 

101.  7 

ii 

10.  O 

4-5 

7' 

64.9 

28.9 

'3' 

119.7 

53-3 

191 

174-5 

77-7 

251 

229.  3 

102.  I 

12 

II.  O 

4-9 

72 

65.8 

29-3 

32 

120.  6 

53-7 

92 

175-4 

78.1 

52 

330.  2 

102.  5 

13 

II.  Q 

5-3 

73 

66.  7 

29-7 

33 

121.5 

54.1 

93 

176-3 

78.5 

53 

23I.I 

102.  9 

H 

12.8 

5-7 

74 

67.6 

30.1 

34 

122.  4 

54-5 

94 

177.2 

78.9 

54 

232.  o 

I03-  3 

15 

13-7 

6.  I 

75 

68.5 

30.5 

35 

123-3 

54-9 

95 

178.  i 

79-3 

55 

233-0 

i°3-  7 

to 

14-6 

6-5 

76 

69.4 

30-9 

36 

124.  2 

55-3 

96 

179.  I 

79-7 

56 

233-9 

104.  i 

17 

"5-5 

6.9 

77 

70-3 

3r-3 

37 

125.  2 

55-7 

97 

iSo.  o 

80.  i 

57 

234-8 

104.5 

18 

16.4 

7-3 

78 

7'-  3 

31-7 

38 

126.  I 

56.1 

98 

180.9 

80.  5 

58 

235-7 

104.9 

rg 

17.4 

7-7 

79 

72.2 

32.1 

39 

127.  o 

56.5 

99 

181.8 

80.  9 

59 

236.  6 

105-3 

20 

18.  3 

8.1 

So 

73-  ' 

32-5 

40 

127.9 

56.9 

200 

182.  7 

Si-  3 

60 

237.5 

105.8 

21 

19.2 

8-5 

81 

74-o 

32-9 

141 

128.8 

57-3 

201 

183.6 

81.8 

261 

238-4 

106.  2 

22 

20.  I 

8.9 

82 

74-9 

33-4 

42 

129.7 

57.8 

02 

184.5 

82.2 

62 

239-3 

106.  6 

23 
24 

21.0 
21.9 

9-4 
9-8 

f3 
84 

*! 

33-8 
34-2 

43 
44 

130.6 
I3I.6 

56.2 
58.6 

°3 

04 

185.4 
186.4 

82.6 
83.0 

63 
64 

240.3 

241.  2 

107.0 

107-4 

25 
26 

22.8 
23.8 

IO.  2 

10.  6 

85 
86 

%i 

34-6 
35-o 

45 
46 

I32-5 
133-4 

59-o 
59-4 

05 
06 

187-3 
188.2 

83-4 
83.8 

8 

242.  I 
243-0 

107.8 
108.2 

27 

24-7 

II.  O 

87 

79-5 

35-4 

47 

'34-3 

07 

189.  i 

84.  2 

67 

243-9 

108.6 

28 

25.6 

11.4 

88 

80.4 

35-8 

48 

'35-2 

60.  2 

08 

190.  o 

84.6 

68 

244.8 

109.  o 

29 

26.5 

11.  8 

89 

81.3 

36.  2 

49 

136.  I 

60.6 

09 

iqo.  9 

85.0 

69 

245-7 

109.  4 

3° 

27.4 

12.  2 

9° 

82.  2 

36.6 

So 

137-0 

61.  o 

10 

191.8 

85.4 

70 

246.7 

109.  8 

31 

28.3 

12.6 

QI 

83.1 

37-o 

151 

137-9 

61.4 

211 

192.8 

85.8 

271 

247.6 

no.  2 

3* 

29.  2 

13.0 

92 

84.0 

37-4 

52 

138.9 

61.8 

12 

193.7 

86.2 

72 

248.5 

1  10.  6 

33 

3O.I 

13-4 

93 

85.0 

37-8 

53 

139-8 

62.  2 

13 

194.6 

86.6 

73 

249.  4 

III.  O 

34 

13-8 

94 

85.9 

38.2 

54 

140-  7 

62.6 

14 

195-5 

87.0 

74 

250-3 

in.  4 

35 

32.0 

14.2 

95 

86.8 

38.6 

55 

141.  6 

63.  o 

IS 

196.4 

87.4 

75 

251.  2 

in.  9 

36 

32-9 

14.  6 

96 

87.7 

39-o 

56 

142.5 

63-5 

16 

197-3 

87.9 

76 

252.  I 

112.3 

37 

33-8 

15.0 

97 

88.6 

39-5, 

57 

143-4 

63.  9 

17 

198.2 

88.3 

77 

253-1 

112.7 

38 

34-7 

98 

89-5 

39-9 

58 

144-3 

64-3 

18 

199.2 

GS-7 

78 

254.0 

113-1 

39 

35-  6 

15.9 

99 

90.4 

40-3 

59 

145-3 

64.  7 

19 

200.  I 

89.  i 

79 

254.9 

"3-5 

40 

36-  5 

16.3 

IOO 

91.4 

40.  7 

60 

146.  2 

65.1 

20 

2OI.  O 

89-5 

80 

255.8 

»3.9 

41 

37-5 

16.7 

IOI 

92-3 

41.1 

161 

147.  I 

65.5 

221 

201.  9 

89.9 

281 

256.7 

"4-3 

42 

3s-  4 

17.  i 

02 

93-2 

41.5 

62 

148.0 

65.9 

22 

202.  8 

90.3 

82 

257.6 

114.7 

43 

39-3 

"7-5 

03 

94-  I 

41.9 

63 

148.9 

66.3 

23 

203.7 

90.  7 

83 

258.5 

115.1 

44 

40.  2 

"7-9 

04 

95-o 

42-3 

64 

M9-  8 

66.  7 

24 

204.  6 

91.  i 

84 

259.4 

"5-5 

45 

41.  I 

18.3 

05 

95-9 

42-  7 

65 

150.7 

67.1 

25 

205.5 

91.5 

85 

260.  4 

115.9 

46 

42.  o 

18.7 

06 

96.8 

43-' 

66 

151.  6 

67-5 

26 

206.  5 

91.9 

86 

261.  3 

116.  3 

47 

42.9 

19.  i 

°7 

97-7 

43-5 

67 

152.  6 

67.9 

27 

207.4 

92-3 

87 

262.  2 

116.  7 

48 

43-9 

19.5 

08 

98.7 

43-9 

68 

153-5 

68.3 

28 

208.3 

92-7 

88 

263.  i 

117.1 

49 

44-8 

19.9 

09 

99.6 

44-3 

69 

154-4 

68.7 

29 

209.  2 

93-1 

89 

264.  o 

117.5 

5° 

45-7 

20.  3 

10 

loo.  5 

44-  7 

70 

155-3 

69.  i 

3° 

210.  I 

93-5 

90 

264.9 

118.0 

51 

46.6 

20.  7 

III 

101.  4 

45.  i 

171 

156.  2 

69.  6 

231 

211.  O 

94.0 

291 

265.8 

118.4 

52 

47-5 

21.  2 

12 

1  02.  3 

45-6 

72 

I57.I 

70.  o 

S2 

211.  9 

94-4 

92 

266.8 

118.  8 

53 

48-4 

21.6 

'3 

103.  2 

46.  o 

73 

158.0 

70.4 

33 

212.  9 

94-8 

93 

267.7 

119.  2 

54 

49-3 

•22.  O 

104.  i 

46.4 

74 

159.0 

70.8 

34 

213.8 

95-2 

94 

268.6 

119.  6 

55 

50.  2 

22.4 

15 

105.  i 

46.8 

75 

159.9 

71.2 

35 

214.  7 

95.6 

95 

269.5 

1  2O.  O 

56 

51.2 

22.8 

16 

1  06.  o 

47-2 

76 

160.8 

71.6 

36 

215.  6 

96.  o 

96 

270.4 

1  20.  4 

57 

52.1 

23.2 

17 

1  06.  9 

47-6 

77 

161.  7 

72.  o 

37 

216.  5 

96.4 

97 

271.3 

120.8 

58 

23.  6 

18 

107.8 

48.0 

78 

162.  6 

72.4 

38 

217.4 

96.8 

98 

272.  2 

121.  2 

59 

53-9 

24.  o 

19 

loS.  7 

48.4 

79 

163-5 

72.8 

39 

218.3 

97-2 

99 

273-2 

121.  6 

60 

54-8 

24.4 

20 

109.  6 

48.8 

So 

164.4 

73-2 

40 

219-3 

97.6 

300 

274-  t 

122.0 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  66  Degrees. 

137 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  25°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.4 

61 

55-3 

25.8 

121 

109.  7 

SI-' 

181 

164.0 

76-5 

241 

218.4 

IQJ.  9 

2 

1.8 

0.8 

62 

56.2 

26.  2 

22 

no.  6 

5'-  6 

82 

164.9 

76.9 

42 

219.3 

102.3 

3 

2-7 

'•3 

63 

57.i 

26.6 

23 

in.  5 

52.0 

83 

165.9 

77-3 

43 

220.  2 

102.  1 

4 

3-6 

64 

58.0 

27.0 

24 

112.  4 

52.4 

84 

166.  8 

77-8 

44 

221.  I 

103.  i 

5 

4-5 

2.  1 

65 

58-9 

27-5 

25 

"3-3 

52.8 

85 

167.7 

78.2 

45 

222.  O 

103-5 

6 

5-4 

2-5 

66 

59-8 

27-9 

26 

114.  2 

53-2 

26 

168.6 

78.6 

46 

223.0 

104.0 

7 

6-3 

3-° 

67 

60.7 

4  3 

27 

115.  I 

53-7 

87 

169-5 

79-0 

47 

223.  9 

104.4 

8 

7-3 

3-4 

68 

61.6 

28.7 

28 

1  16.  0 

54-1 

88 

170.4 

79-5 

48 

224.  8 

104.8 

9 

8.  2 

3-8 

69 

62.5 

29.  2 

29 

1  16.  9 

54-5 

89 

I7I-3 

79-9 

49 

225.7 

105.  2 

10 

9-  i 

4-2 

7° 

63-4 

29.  6 

3° 

117.8 

54-9 

90 

172.2 

So.  3 

5° 

226.6 

105.  7 

II 

IO.  O 

4.6 

7' 

64.  3 

30.  o. 

'3' 

118.  7 

55-4 

191 

1  73-  i 

80.7 

251 

227.5 

1  06.  i 

12 

10.9 

5.  I 

72 

65.3 

30.4 

32 

119.  6 

55-8 

92 

174.0 

81.  i 

52 

228.4 

1  06.  5 

'3 

n.  8 

5-5 

73 

66.2 

3°-9 

33 

120.  5 

55.2 

93 

174.9 

81.6 

53 

229.3 

106.  9 

H 

12.7 

5-9 

74 

67.1 

3'-3 

34 

121.4 

56.6 

94 

175.8 

82.0 

54 

230.2 

107-3 

IS 

13.6 

6.3 

75 

68.0 

3'-  7 

35 

122.4 

57-1 

95 

176.7 

82.4 

55 

231.  I 

107.  8 

16 

14.5 

6.8 

76 

68.9 

32.1 

36 

123.3 

57-5 

96 

177.6 

82.8 

56 

232.  o 

108.2 

17 

'5-4 

7-2 

77 

69.8 

32-5 

37 

124.  2 

57-9 

97 

'7S-5 

83-3 

57 

232.9 

108.6 

18 

16.3 

7.6 

78 

70.7 

33-  ° 

38 

125.  I 

58.3 

98 

179.4 

83-7 

58 

233-8 

109.  o 

19 

17.2 

8.0 

79 

71.6 

33-4 

39 

126.  o 

58.7 

99 

180.4 

84.1 

59 

234-  7 

109.5 

20 

18.  i 

8-  5 

80 

72.5 

33-8 

40 

126.9 

59-2 

200 

181.3 

84-  S 

Bo 

235.6 

109.9 

21 

19.  o 

8.9 

Si 

73-4 

34-2 

141 

127.8 

59-6 

201 

182.2 

84.9 

261 

236-5 

110.3 

22 

19.9 

9-3 

82 

74-3 

34-7 

42 

1  2&.  7 

60.  o 

O2 

183.  i 

«5-4 

62 

237-5 

no.  7 

23 

20.8 

9-7 

83 

75-2 

35-1 

43 

129.  6 

60.  4 

°3 

184.0 

85.8 

63 

238-4 

in.  i 

24 

21.8 

10.  I 

84 

76.1 

35-5 

44 

130-5 

60.  9 

04 

184.9 

86.2 

64 

239-3 

in.  6 

25 

22.7 

10.  6 

85 

77-0 

35-9 

45 

61.3 

°5 

185.8 

86.6 

65 

240.  2 

112.  O 

26 

23.6 

II.  O 

86 

77-9 

36.3 

46 

I32-3 

61.7 

06 

186.7 

87.1 

66 

241.  I 

112.4 

27 

24.5 

II.  4 

87 

78.8 

36.8 

47 

133-2 

62.1 

°7 

187.6 

87-5 

67 

242.  o 

II2.8 

28 

25.4 

n.  8 

88 

79.8 

37-2 

48 

I34-I 

62.5 

08 

1  88.  5 

87-9 

68 

242-9 

"3.3 

29 

26.3 

12.3 

89 

80.7 

37-6 

49 

i35-o 

63.  o 

09 

189.4 

88.3 

69 

243-8 

"3-7 

30 

27.2 

12.7 

9° 

81.6 

38.0 

5° 

'35-9 

63-4 

10 

190.  3 

88.  7 

70 

244-  7 

114.1 

31 

28.1 

13.  i 

91 

82.5 

38.5 

'51 

136.9 

63.8 

211 

191.  2 

89.2 

271 

245-6 

JI4-5 

32 

29.  o 

13-5 

92 

38-9 

52 

137-8 

64.  2 

12 

192.  I 

89,6 

72 

246-  5 

115.  o 

33 

29.9 

I3.9 

93 

84'  3 

39-3 

53 

138.  7 

64.  7 

'3 

193.0 

90.  o 

73 

247.4 

115.4 

34 

3".  8 

14.4 

94 

85.2 

.39-7 

54 

139.6 

65.1 

"93-9 

90.4 

74 

248.3 

115.8 

35 

3'-7 

14.8 

95 

86.  i 

40.  i 

55 

140.5 

65.5 

15 

194.  9 

90-9 

75 

249.2 

116.  2 

36 

32.  6 

15.2 

96 

87.0 

40.  6 

5& 

141.4 

65.9 

16 

195.8 

9'-3 

76 

250.  i 

116.6 

37 

33-5 

15.6 

97 

87.9 

41.0 

57 

142-3 

66.4 

'7 

196-  7 

91.7 

77 

251.0 

117.1 

38 

34-4 

16.  i 

98 

88.8 

4'-4 

58 

143-2 

66.8 

18 

197.6 

92.1 

78 

252.  o 

117.5 

39 

35-3 

16.5 

99 

89-7 

41.8 

59 

144.  i 

67.2 

19 

198-5 

92.  6 

79 

252.  9 

117.9 

40 

36-3 

16.9 

100 

90.  6 

42.3 

60 

145.0 

67.6 

20 

199.4 

93-° 

80. 

253-8 

1  18.  3 

4' 

37-2 

'7-3 

101 

91.5 

42-7 

i&i 

145.9 

68.0 

221 

200.  3 

93-4 

281 

254-7 

118.  8 

42 

38.1 

'7-7 

02 

92.4 

43-1 

62 

146.8 

6S.  5 

22 

201.  2 

93-8 

82 

255-6 

119.2 

43 

39-o 

18.  2 

03 

93-3 

43-5 

63 

147-7 

68.9 

23 

202.  I 

94-2 

83 

256-5 

119.  6 

44 

39-9 

18.  6 

04 

94-3 

44.0 

64 

148.6 

69-3 

24 

203.  o 

94-7 

84 

257-4 

120.0 

45 

40.8 

19.  o 

05 

95-2 

44-4 

65 

149.5 

69.  7 

25 

203.  9 

95-  « 

85 

258-3 

120.4 

46 

41.7 

19.4 

06 

96.  i 

44-8 

66 

150.4 

70.2 

26 

204.  8 

95-5 

86 

259.2 

1  20.  9 

47 

42.  6 

19.9 

07 

97.0 

45.2 

67 

15L4 

70.  6 

27 

205-7 

95-9 

87 

260.  i 

121.3 

48 

43-5 

20.  3 

08 

97-9 

45.6 

68 

'52-3 

71.0 

28 

206.  6 

96.4 

88 

261.  o 

121.7 

49 

44-4 

20.  7 

09 

98.8 

46.1 

69 

153.2 

71.4 

29 

207.5 

96.8 

89 

261.  9 

122.  I 

50 

45-3 

21.  I 

10 

99-  7 

46.5 

70 

K4-  ' 

71.8 

208.5 

97-2 

90 

262.8 

122.  6 

51 

46.2 

27.6 

III 

loo.  6 

46:9 

171 

155-0 

72.3 

23' 

209.4 

97-6 

291 

263.7 

123.0 

52 

47-' 

22.0 

12 

101.5 

47-3 

72 

'55-9 

72.7 

32 

210.  3 

98.0 

92 

264.  6 

123-4 

53 

48.0 

22.4 

'3 

102.4 

47-8 

73 

156.8 

73-' 

33 

211.  2 

98.5 

93 

265.  5 

123-8 

54 

48.9 

22.8 

'4 

103-3 

48.2 

74 

'57-7 

73-5 

34 

212.  I 

98.9 

94 

266.  5 

124.2 

55 

49-8 

23.2 

15 

104.  2 

48.6 

75 

158.6 

74.0 

35 

213.0 

99-3 

95 

267-4 

124.7 

56 

50.8 

23.7 

10 

IOC.  I 

49-0 

76 

'59-5 

74-4 

36 

213.  9 

99-7 

96 

268.3 

125.  I 

57 

5'-  7 

24.1 

'7 

100.  0 

49-4 

n 

160.4 

74-8 

37 

214.  8 

IOO.  2 

97 

269.  2 

125.  5 

58 

52.6 

24.5 

18 

1  06.  9 

49.9 

78 

161.3 

75.2 

3» 

215.  7 

100.  6 

98 

27O.  I 

125.9 

11 

53-5 
54-4 

2419 
25-4 

20 

107.  0 

108.8 

50.3 
50.7 

79 

So 

162.2 
163.  i 

a; 

39 
40 

216.6 
217.5 

101.  0 

101.4 

99 

300 

271.0 
271.9 

126.4 
126.8 

Plot. 

Dep. 

Ut. 

Diit, 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Diet. 

Dep. 

Lit. 

[I'*  or  65  Degree*. 

188 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2G°. 

Dist. 

Lat, 

Dep. 

Dist. 

Lat. 

Dep. 

DisL 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.4 

6l 

54-8 

26.7 

121 

108.  8 

53-  ° 

181 

162.  7 

79-3 

24" 

216.6 

105.  6 

2 

1.8 

0.9 

62 

55-7 

27.2 

22 

109.7 

53-  5 

82 

163.6 

79.8 

42 

217.5 

1  06.  I 

3 

2.7 

I.  3 

63 

56.6 

27.6 

23 

no.  6 

53-9 

83 

164-5 

So.  2 

43 

218.4 

1  06.  5 

4 

3-6 

i.  8 

64 

57-5 

28.1 

24 

111.5 

54-4 

84 

165.4 

So.  7 

44 

219-3 

107.  o 

5 

4-5 

2.  2 

65 

58-4 

28.5 

25 

112.  3 

54-8 

85 

166.3 

81.  i 

45 

220.  2 

107.4 

6 

5-4 

2.6 

66 

59-3 

28.9 

26 

113.2 

SS-2 

86 

167.  2 

8..  5 

46 

221.  I 

107.8 

7 

6-3 

3-' 

67 

60.  2 

29.4 

27 

114.  i 

55-7 

87 

1  68.  i 

82.0 

47 

222.  0 

108.3 

8 

7.2 

3-  5 

68 

61.  i 

29.8 

28 

115.  o 

56.1 

88 

169.  o 

82.4 

48 

222.  9 

1  08.  7 

9 

8.1 

3-9 

69 

62.  o 

30.2 

29 

115.9 

56-5 

89 

169.9 

82.  9 

49 

223.8 

109.  2 

10 

9.0 

4-4 

7° 

62.  9 

3°-7 

3° 

116.  8 

57-o 

90 

170.8 

83-3 

5° 

224.  7 

109.  6 

11 

9-9 

4.8 

7' 

63.8 

31-  ' 

131 

117.7 

57-4 

IO"I 

171.  7 

83-7 

251 

225.  6 

HO.  O 

12 

10.8 

5-3 

72 

64.7 

31-6 

32 

118.  6 

57-9 

52 

172.  6 

84.2 

52 

226.  5 

HO.  5 

13 

u.  7 

5-7 

73 

65.6 

32.0 

33 

119.5 

58-3 

93 

'73-5 

84.6 

53 

227-4 

HO.  9 

«4 

12.6 

6.  i 

•74 

66.  3 

32-4 

34 

120.  4 

58.7 

94 

174.4 

85.0 

54 

228.3 

in.  3 

15 

'3-5 

6.6 

75 

67-4 

32-9 

35 

121.3 

59-2 

95 

«75-3 

85.5 

55 

229.  2 

in.  8 

16 

14.4 

7.0 

76 

68.3 

33-3 

36 

122.  2 

59-6 

96 

176.  2 

85.9 

56 

230-  1 

112.  2 

'7 

'5-3 

7-5 

77 

69.  2 

33-8 

37 

I23.I 

60.  i 

97 

I77.I 

86.4 

57 

231.0 

II2.7 

18 

16.  2 

7-9 

73 

70..I 

34-2 

38 

124.  o 

60.  5 

98 

178.0 

86.8 

58 

23'-9 

II3.I 

'9 

"7-  i 

8.3 

I9 

71.0 

34-6 

39 

124.9 

60.  9 

99 

178.9 

87.2 

59 

232.  8 

"3-5 

20 

18.  o 

8.8 

So 

71.9 

35-  i 

46 

125.8 

61.4 

200 

179.8 

87.7 

60 

233-7 

114.0 

21 

iS.  9 

9.2 

81 

72.S 

35-5 

141 

126.  7 

61.8 

201 

180.  7 

88.  i 

261 

234-6 

114.4 

22 

19.8 

9.6 

82 

73-7 

35-9 

42 

127.  6 

62.2 

O2 

181.6 

88.6 

62 

235-5 

114.9 

23 

20.7 

IO.  I 

83 

74.6 

36-4 

43 

128.5 

62.7 

°3 

182.5 

89.0 

63 

236.4 

"5-3 

24 

21.6 

10.5 

84 

75-5 

36.8 

44 

129.4 

63.1 

04 

183.  4 

89.4 

64 

237-3 

115.7 

25 

22.5 

II.  O 

85 

76.4 

37-3 

45 

'3°-3 

63.6 

05 

184.3 

89.9 

65 

238.2 

116.  2 

26 

23-4 

11.4 

86 

77-3 

37-7 

46 

131.2 

64.  o 

06 

185.2 

9°-3 

66 

239-  ' 

116.6 

27 

24-3 

n.  8 

87 

78.2 

38-1 

47 

132.1 

64-4 

07 

1  86.  i 

90.7 

67 

240.  o 

117.  o 

28 

25.  2 

12.3 

88 

79-  i 

38.6 

48 

«33-° 

64.9 

08 

1  86.  9 

91.2 

68 

240.9 

«'7-5 

29 

26.  I 

12.7 

89 

So.  o 

39-o 

49 

«33-9 

65-3 

09 

187.8. 

91.  6 

69 

241.8 

117.9 

3° 

27.  o 

n.  2 

90 

80.9 

39-5 

5° 

134.8 

65.8 

IO 

1  88.  7 

92.  i 

70 

242.7 

118.4 

31 

27.9 

13.  b 

9' 

81.8 

39-9 

'5' 

«35-7 

66.2 

211 

189.6 

92.5 

271 

243.6 

nS.  8 

32 

28.8 

14.  o 

92 

82.7 

4°-3 

52 

136.6 

66.6 

12 

190.5 

92.9 

72 

244.5 

119.  2 

33 

29.7 

14.5 

93 

83.6 

40.  8 

53 

»37-5 

67.1 

13 

191.4 

93-4 

73 

245-4 

119.7 

34 

30.6 

14.9 

94 

84.5 

41.2 

54 

138.4 

67-5 

14 

192.3 

93-8 

74 

246.3 

120.  I 

35 

3^-5 

15-3 

95 

85.4 

41.6 

55 

'39-3 

67.9 

IS 

193.2 

94-2 

75 

247.2 

1  20.  6 

36 

32-4 

15.8 

96 

86.3 

42.1 

56 

140.  2 

68.4 

16 

194.  i 

94-7 

76 

248.  1 

121.  0 

37 

33-3 

1  6.  2 

97 

87.2 

42.5 

57 

14:.  I 

68.8 

17 

195.0 

95.1 

77 

249-  ° 

I2I.4 

38 

34-2 

16.7 

98 

88.  i 

43-  ° 

58 

142.  o 

69-3 

18 

«95-9 

95-6 

78 

249-9 

121.  9 

39 

35-  > 

17.  1 

99 

89.0 

43-4 

59 

142.9 

69.7 

19 

196.  8 

96.  o 

79 

250.8 

122-3 

40 

36.  o 

'7-5 

IOO 

89.9 

43-8 

60 

I43.S 

70.  i 

20 

197.7 

96.4 

80 

251.7 

122.7 

41 

36-9 

1  8.  o 

101 

90.  8 

44-3 

161 

144.  7 

70.  6 

221 

198.6 

96.9 

281 

252.  6 

123.2 

42 

37-7 

18.4 

02 

91-7 

44-  7 

62 

MS'6 

71.0 

22 

J99-5 

97-3 

82 

253-5 

123.  6 

43 

38.6 

18.  8 

°3 

92.  6 

45-2 

63 

146.5 

71-5 

23 

200.  4 

97.8 

83 

254.4 

124.  i 

44 

39-5 

19-3 

04 

93-5 

45-6 

64 

147.4 

71.9 

24 

201.  3 

98.  2 

84 

255-3 

124-5 

45 

40.4 

"9-7 

°5 

94-4 

46.0 

65 

148.3 

72-3 

25 

202.  2 

98.6 

85 

256.  2 

124.9 

46 

4'-3 

20.  2 

06 

95-3 

46-5 

66 

149.2 

72.8 

26 

203.  I 

99-  i 

86 

257.1 

125.4 

47 

42.2 

20.  6 

07 

96.  2 

46.9 

67 

150.  i 

73-2 

27 

204.  o 

99-5 

87 

258.0 

125.8 

48 

43-i 

21.  0 

08 

97-  i 

47-3 

68 

151.  o 

73-6 

28 

204.9 

99-9 

88 

258.9 

126.3 

49 

44-° 

21-5 

OQ 

98.0 

47-8 

69 

151.9 

74-1 

29 

205.8 

loo.  4 

89 

259-  8 

126.  7 

5° 

44-9 

21-9 

10 

98.9 

48.  2 

7° 

152.8 

74-5 

30 

206.  7 

100.8 

9° 

260.  7 

127.1 

5' 

45.8 

22.4 

I  II 

9-9.  8 

48.7 

171 

153-7 

75.0 

231 

207.  6 

101.  3 

291 

261.  5 

127.  6 

S2 

46-7 

22.8 

12 

loo.  7 

49-  ' 

72 

154.6 

75-4 

32 

208.5 

101.  7 

92 

262.  4 

128.0 

53 

47-6 

23.2 

'3 

101.  6 

49-5 

73 

'55-5 

75-8 

33 

209.4 

102.  I 

93 

263-3 

128.4 

54 

48.5 

23-7 

H 

102.  5 

50.  o 

74 

156.4 

76-3 

34 

210.  3 

102.  6 

94 

264.  2 

128.9 

55 

49-4 

24.  I 

15 

103.4 

5°-4 

75 

J57-  3 

76.7 

35 

211.  2 

103.  o 

95 

265.1 

129-3 

56 

50.3 

24-5 

1  6 

104.3 

50.9 

76 

158.2 

77-2 

36 

212.  I 

«°3-5 

96 

266.  o 

129.  8 

57 

51.2 

25.  o 

17 

105.  2 

5'-3 

77 

159.  i 

77-6 

37 

213.  o 

i°3-9 

97 

266.  9 

130.  2 

58 

52-1 

25.4 

18 

1  06.  I 

5'-7 

78 

100.  0 

78.0 

38 

213-9 

104-3 

9« 

•267.8 

130.  6 

59 

53-  ° 

25-9 

"9 

107.  o 

52.2 

79 

1  60.  9 

78.5 

39 

214.8 

104.  8 

99 

268.7 

iji.  i 

60 

53-9 

26.  3 

20 

107.9 

52.6 

So, 

161.8 

78.9 

40 

215.7 

105.2 

300 

269.  6 

'3'-5 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  64  Degrees. 

loU 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  27°. 

Dist. 

Lat. 

Dcp. 

Dibt. 

Lat. 

Dcp. 

Dist. 

I-at. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.5 

61 

54-4 

27.7 

121 

107.8 

54-9 

181 

161.3 

82.2 

241 

214.  7 

109.4 

2 

1.8 

0.9 

62 

55-2 

28.1 

22 

108.  7 

55-4 

82 

162.  2 

82.6 

42 

215.  6 

109.9 

3 

2.  7 

1-4 

63 

56., 

28.6 

23, 

109.  6 

55-8 

83 

163.  I 

83.1 

43 

216.  5 

1  1  0-3 

4 

3-6 

1.8 

64 

57.0 

29.  I 

2.A 

**r 

no.  5 

56-3 

84 

163.9 

83-5 

44 

217.4 

no.  8 

5 

4-5 

2-3 

65 

57-9 

29-5 

25 

ill.  4 

56.7 

85 

164.8 

84.  o 

45 

218.3 

III.  2 

6 

5-3 

2-7 

66 

58.8 

30.  o 

26 

112.  3 

57-2 

S6 

165.7 

84.4 

46 

219.  2 

III.7 

7 

6.2 

3-2 

67 

59-7 

3°-4 

27 

113.2 

57-7 

27 

i65.  6 

84-9 

47 

22O.  I 

112.  I 

8 

7-i 

3-6 

68 

60.6 

3°-9 

28 

114.  o 

53.  i 

S8 

167.5 

85-4 

48 

221.  O 

112.  6 

9 

8.0 

4-  i 

69 

61.5 

3'-3 

29 

1  14.  9 

58.6 

89 

168.4 

85.8 

49 

221.  9 

113.  o 

10 

8.9 

4-5 

7° 

62.4 

31.8 

3° 

115.8 

59-o 

90 

169.  3 

86.  3 

5° 

222.8 

"3-5 

II 

9.8 

5.0 

?i 

63-3 

32'  2 

«3> 

116.  7 

59-5 

191 

170.  2 

86.  7 

251 

223.  6 

114.0 

12 

10.7 

5-4 

72 

64.2 

32-7 

32 

117.  6 

59-9 

92 

I7I.I 

87.2 

S2 

224-5 

114.4 

13 

u.  6 

5-9 

73 

65.  o 

33-i 

33 

118.  5 

60.  4 

93 

172.  o 

87.6 

5? 

225.4 

114.9 

'4 

I2-5 

6.4 

74 

65.9 

33-6 

34 

119.4 

60.8 

94 

172.9 

88.1 

54 

226.3 

iiS-3 

15 

13-4 

6.8 

75 

66.8 

34-o 

35 

120.  3 

61.3 

95 

173-7 

88.5 

55 

227.  2 

115.8 

16 

14-3 

7-3 

76 

67.7 

34-  5 

36 

21.  2 

61.7 

96 

174.6 

89.0 

56 

228.  I 

1  16.  2 

17 

15.  i 

7-7 

77 

68.6 

35-  ° 

37 

22.  I 

62.2 

97 

'75-5 

89.4 

57 

229.  o 

116.  7 

iS 

16.  o 

8.2 

73 

69.5 

35-4 

3y 

23.0 

62.7 

98 

176.4 

89.9 

58 

229.9 

117.1 

19 

16.  9 

8.6 

79 

70.4 

35-9 

39 

23.8 

63-1 

99' 

177-3 

90.3 

59 

230.8 

117.6 

20 

17.8 

9-  i 

So 

7'-3 

36-  3 

40 

24.  7 

63.6 

200 

178.  2 

90.  8 

60 

231-  7 

118.  o 

21 

18.7 

9-5 

Si 

72.2 

36.8 

141 

25.6 

64.0 

201 

1/9-  l 

9i-3 

261 

232.  6 

118.5 

22 

•19.  6 

lo.  o 

82 

73-  i 

37-2 

42 

26.5 

64.5 

O2 

i  So.  o 

91.7 

62 

233-4 

118.9 

23 

20.  5 

10.  4 

S3 

74.0 

37-7 

43 

127.4 

64.9 

°3 

I  So.  9 

92.2 

6j 

234-3 

119.4 

24 

21.4 

10.  9 

84 

74-  S 

38.1 

44 

128.3 

65.4 

04 

181.8 

92.  6 

64 

235-2 

119.9 

25 

22.  3 

"•3 

85 

75-  7 

38-6 

45 

129.  2 

65.8 

°5 

182.  7 

93-  i 

65 

236.  i 

120.  3 

26 

23.2 

11.8 

86 

76.6 

39-o 

46 

I3O.  I 

66.3 

•06 

183-5 

93-5 

66 

237-0 

120.  8 

27 

24.  I 

12.3 

«7 

77-5 

39-5 

47 

I3I.O 

66.  7 

07 

184.4 

94.0 

67 

237-9 

121.  2 

28 

24.9 

12.7 

SS 

78.4 

40.  o 

48 

'    I3I-9 

67.2 

08 

iSS-3 

94-4 

68 

238.8 

I2I.7 

29 

25.8 

13.2 

89 

79-3 

40.4 

49 

132.8 

67.6 

09 

186,2 

94-9 

69 

239-7 

122.  I 

3° 

26.  7 

13.6 

90 

80.  2 

40.9 

5° 

'33-  7 

68.  i 

10 

187.  i 

95-3 

70 

240.  6 

122.  6 

3' 

27.6 

14.  i 

91 

Si.  i 

4'-3 

IS1 

134.5 

68.6 

211 

188.0 

95-8 

271 

241-5 

123.  o 

32 

28.5 

14-5 

92 

82.0 

41.8 

52 

'35-4 

69.  o 

12 

188.9 

96.  2 

72 

242.4 

123-5 

33 

29.4 

15.0 

93 

82.9 

42.2 

53 

'3<5-  3 

69.5 

'3 

189.8 

96.7 

73 

243-2 

123-9 

34 

3°-3 

15.4 

•   94 

83.8 

42-7 

54 

137-2 

69.9 

H 

190.  7 

97-2 

74 

244.1- 

124.4 

35 

31.2 

15.9 

95 

84.6 

43-  ' 

55 

138.  i 

70.4 

15 

191.  6 

97.6 

75 

245.0 

124.8 

36 

32.1 

16.3 

96 

85.5 

43-  6 

56 

139.0 

70.8 

16 

192-5 

98.  i 

76 

245.9 

I25.  3 

37 

33-° 

16.8 

97 

86.4 

44.0 

57 

'39-9 

71-3 

17 

193-3 

98-5 

77 

246.8 

125.8 

38 

33-9 

17-3 

98 

87-3 

44-5 

58 

140.  8 

71-7 

18 

194.2 

99-o 

78 

247-  7 

126.  2 

39 

34-7 

'7-7 

99 

SS.  2 

44-9 

59 

141.7 

72.2 

19 

195.  i 

99-4 

79 

248.6 

126/7 

40 

35-  6 

IS.  2 

IOO 

89.  I 

4JM 

60 

142.  6 

72.6 

20 

196.  o 

99-9 

80 

249-5 

I27.I 

4' 

36.5 

18.  6 

101 

90.  o 

45-9 

161  ' 

143-5 

73-  i 

221 

196.9 

loo.  3 

281 

250.4 

127.  6 

42 

37-4 

19.1 

02 

90.9 

46-  3 

62 

144-3 

73-5 

22 

197.8 

loo.  8 

82 

251-3 

128.0 

43 

38-3 

19.5 

°3 

91.8 

46.8 

63 

145.2 

71-0 

23 

198.7 

IOI.  2 

83 

252.  2 

128.  5 

44 

39-2 

20.  O 

04 

92-7 

47-2 

64 

146.  i 

74-5 

24 

199.6 

101.  7 

84 

253-0 

128.9 

45 

40.  i 

20.  4 

°5 

93-  6 

47-7 

65 

147.0 

74-9 

25 

200.  5 

102.  I 

85 

253-9 

129.4 

46 

41.  o 

20.  9 

06 

94-4 

48.  i 

66 

147.9 

75-4 

26 

201.  4 

102.  6 

86 

254-8 

129.8 

47 

41.9 

21.  3 

°7 

95-3 

48.6 

67 

148.8 

75-8 

27 

202.  3 

103.  I 

87 

255-7 

130-3 

48 

42.8 

21.8 

08 

96.2 

49.0 

68 

149.  7 

76-3 

28 

203.  I 

103-5 

88 

256.  6 

130-7 

49 

43-7 

22.  2 

09 

97.1 

49-5 

69 

150.  6 

76.7 

29 

204.  o 

104.  o 

89 

257-5 

131.2 

5° 

44.6 

22.  7 

10 

98.0 

40.9 

70 

151.5 

77-2 

3° 

204.9 

104.4 

90 

258.4 

i3i-7 

5' 

45-4 

23.2 

III 

98.9 

50.4 

I?' 

152.4 

77.6 

231 

205.8 

104.9 

291 

259-3 

132.1 

52 

46-3 

23.6 

12 

99-8 

50.8 

y2 

153-3 

78.1 

32 

206.  7 

105-3 

92 

2CO.  2 

132.  6 

53 

47.2 

24.  I 

«3 

loo.  7 

5i-3 

73 

154.1 

78.5 

33 

207.  6 

105.  8 

93 

26l.  I 

133-0 

54 

48.  i 

24-5 

14 

loi.  6 

Si-8 

74 

155-° 

79.0 

34 

208.5 

1  06.  2 

94 

262.  o 

133-5 

55 

49.0 

25.  o 

IS 

1  02.  5 

52.  .2 

75 

155-9 

79-4 

35 

209.4 

1  06.  7 

95 

262.8 

133-9 

56 

49-9 

25.4 

16 

103.4 

52.7 

76 

156.8 

79-9 

36 

210.3 

107.  1 

96 

263.7 

I34.4 

57 

50.8 

25.9 

17 

104.  2 

53-  i 

77 

157-  7 

80.4 

37- 

211.  2 

107.  6 

97 

264.  6 

134.  8 

58 

5'-  7 

26.  3 

18 

105.  I 

53-6 

78 

158.6 

80.8 

38 

212.  I 

108.0 

98 

265.5 

135-3 

59 

52.6 

26.8 

19 

1  06.  o 

31.0 

79 

159-5 

81.3 

39 

213.  o 

1  08.  5 

99 

266.4 

135-7 

60 

53-5 

27.2 

20 

106.  9 

54-5 

80 

1  60.  4 

81.7 

40 

213.8 

109.  o 

300 

267.3 

136.  2 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Di5t. 

Dep. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lot. 

[  For  63  Degrees. 

140 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  28°. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

I-at 

Dep. 

I 

0.9 

0.  5 

61 

53-9 

28.  6 

121 

Ic6.  8 

56.  8 

iSi 

159.8 

85.  0 

241 

212.  8 

II3.  I 

2 

1.8 

0.9 

62 

54-  7 

29.  I 

22 

107.  7 

57-3 

82 

1  60.  7 

85.4 

42 

213.  7 

113.6 

3 

2.6 

1.4 

63 

55-6 

29.  6 

23 

108.  6 

57-7 

83 

161.6 

85.9 

43 

214.  6 

I  14.  I 

4 

3-5 

1.9 

64 

56-  i 

30.  o 

24 

109.  5 

58.2 

84 

162.  5 

86.4 

44 

215.4 

114.  6 

5 

4-4 

2-  3 

65 

57-4 

3°-5 

25 

1  10.  4 

58.7 

85 

163-3 

86.9 

45 

216.  3 

115.  o 

6 

5-  3 

2.8 

66 

31.0 

26 

111.3 

59-2 

86 

164.  2 

87.3 

46 

217.  2 

115.5 

7 

6.  2 

3-  3 

6? 

59-2 

31-5 

27 

112.  I 

59-6 

87 

165.  I 

87.8 

47 

218.  i 

I  ID.  O 

8 

7-  i 

3-8 

6$ 

60.  o 

31-9 

28 

113.  o 

DO.  I 

88 

166.  o 

88-3 

48 

219.  o 

116.  4 

9 

7-9 

4-2 

69 

60.9 

32-4 

29 

H3-9 

60.  6 

89 

166.9 

88.7 

49 

219.9 

116.  9 

IO 

8.8 

4-  7 

70 

6!.  8 

33-9 

30 

II4.8 

61.  o 

CO 

167.8 

80.2 

50 

220.  7 

117.4 

ii 

9-  7 

5-  2 

7' 

62.7 

33-3 

I3l 

II5.7 

61.5 

191 

168.  6 

89.7 

251 

221.  6 

117.8 

12 

io.-6 

5.6 

72 

63.6 

33-8 

32 

116.  5 

62.  o 

92 

169.5 

90.  i 

52 

222.  5 

118.3 

13 

H.J 

6.  i 

73 

64.5 

34-3 

33 

117.4 

62.  4 

93 

170.4 

90.  6 

53 

223.4 

118.  8 

'4 

12.4 

6.6 

74 

65-3 

34-7 

34 

118.  3 

62.  9 

94 

I7I-3 

91.1 

54 

224-3 

Iig.  2    . 

\l 

13-2 
14.1 

7-5 

75 

66.  2 
67.1 

35-2 
35-  7 

35 
36 

I  19.  2 
120.   I 

63.4 
63.  8 

9 

172.  2 
173-  ' 

91.5 
92.  o 

55 
56 

225.  2 
220.  O 

"9-7 
120.  2 

17 

15.0 

8.0 

77 

6S.o 

36.1 

37 

121.  O 

64-3 

97 

1/3-9 

92.5 

57 

226.  9 

120.  7 

18 

'5-9 

8-5 

78 

•68.9 

36.6 

121.  S 

64.8 

98 

174.8 

93-  ° 

58 

227.8 

121.  I 

'9 

20 

16.8 
17.7 

8.  9 
9-4 

79 
So 

69.8 
70.  6 

37-1 
37-6 

39 

40 

122.  7 

123.  6 

65-3 
65-7 

99 
200 

1/5-  7 
176.  6 

93-  4 
93-9 

S 

228.  7 
229.  6 

121.  6 
122.  I 

21 

18.5 

9-9 

Si 

71-5 

38.0 

141 

124.5 

66.2 

201 

177-5 

94-4 

261 

230-4 

122.5 

22 

19.4 

10.3 

82 

72.4 

3»-5 

42 

125.4 

66.  7 

O2 

178.4 

94-8 

62 

231-3 

123.  o 

23 

20.3 

10.8 

83 

73-3 

39-0 

43 

126.3 

67.1 

03 

179.  2 

95-3 

63 

232.  2 

I23-5 

24 

Si.  2 

"•3 

84 

74-2 

39-4 

44 

127.1 

67.6 

04 

180.  i 

95.8 

64 

233-   I 

I23-9 

25 

22.  I 

11.7 

85 

75-  i 

39-  9 

45 

128.0 

68.  i 

°5 

181.  o 

96.  2 

65 

234.0 

124.4 

26 

23.0 

12.  2 

86 

75-9 

40.4 

46 

128.  9 

68.  5 

06 

181.  9 

96.7 

66 

234-9 

124.9 

27 

23.8 

12-7 

87 

76.8 

40.8 

47 

129.8 

69.  o 

07 

182.8 

97-  2 

67 

235-  7 

28 

.24.7 

"3-' 

88 

77-7 

41-3 

48 

13°-  7 

69.5 

08 

183.7 

97-7 

68 

236.  6 

I2J8 

29 

25.6 

13-6 

89 

78.6 

41.8 

49 

131.  6 

70.  o 

09 

184.5 

98.  i 

69 

237-  5 

126.  3 

3° 

26.5 

14.  i 

90 

79-5 

42-3 

5° 

132-4 

70.4 

10 

185.4 

98.6 

70 

238.4 

126.  8 

3' 

27.4 

14.  6 

9' 

80.3 

42.  7 

I51 

133-3 

70.  9 

211 

186.  3 

99-  i 

271 

239-3 

127.2 

S2 

28.3 

15.0 

92 

81.2 

43-2 

134-2 

71.4 

12 

187.  2 

99-  5 

72 

240.  2 

127.  7 

33 

29.1 

'5-5 

93 

82.  i 

43-7 

53 

135-  i 

71.8 

13 

1  88.  i 

IOO.  O 

73 

241.  o 

128.  2 

34 

30.  o 

IO.  O 

94 

83.  o 

44-  i 

54 

136.  o 

72-3 

14 

189.  o 

too.  5 

74 

241.  9 

28.6 

35 

3°-9 

16.  4 

95 

83.  9 

44-  6 

55 

136.9 

72.8 

15 

lag.  8 

loo.  9 

75 

242.  8 

£9.  i 

36 

31-8 

16.  9 

96 

84.8 

45-  i 

56 

137-7 

73-2 

IO 

190.  7 

101.  4 

76 

243-  7 

29.6 

37 

32-7 

17.4 

97 

£5.  6 

45-5 

57 

138.6 

73-  7 

17 

191.  6 

101.  9 

77 

244.  6 

30.0 

38 

33-6 

17.8 

98 

86.5 

46.  o 

58 

!39-J 

74-2 

18 

192.5 

102.  3 

78 

*45-  5 

30-5 

39 

34-4 

18.3 

99 

87.4 

46-5 

59 

140.4 

74-6 

19 

193-4 

102.  8 

79 

246.  3 

31-0 

40 

35-3 

18.  8 

IOO 

88.3 

46.9 

60 

141-3 

75-  i 

20 

194.  2 

i°3-3 

80 

247-2 

131-5 

41 

36-2 

19.  2 

101 

89.  2 

47-4 

161 

142.  2 

75-6 

221 

195.  i 

103.8 

281 

248.  i 

13I-9 

42 

37-i 

19.  7 

02 

90.  I 

47-9 

62 

143.0 

76.1 

22 

196.  o 

104.  2 

82 

249.  o 

132-4 

43 

38.0 

20.  2 

°3 

90.  9 

48-4 

63 

143-9 

76.5 

23 

196.9 

104.  7 

83 

249.  9 

132.9 

44 

38.8 

20-7 

04 

91.8 

48.8 

64 

144.8 

77-0 

24 

197.8 

105.  2 

84 

250.  8 

133-3 

45 

46 

39-7 
40.  6 

21.  I 
21.6 

05 
06 

92.7 
93.6 

49-3 
49-8 

a 

145-7 

146.  6 

77-5 
77-9 

25 
26 

198.7 

199-  5 

105.  6 
1  06.  I 

85 
86 

251.  6 
252-5 

133-8 
134-3 

47 

41.5 

22.  I 

07 

94-5 

50.  2 

67 

147-5 

78-4 

27 

200.  4 

106.  6 

87 

253-  4 

134-  7 

48 

42.4 

22-5 

08 

95-4 

50.7 

68 

148.3 

78.9 

28 

201.  3 

107.  o 

88 

254-3 

135-2 

49 

43-3 

23.  o 

09 

96.  2 

51.2 

69 

149.2 

79-  3 

29 

2C2.  2 

107.  5 

89 

255-  2 

135-  7 

50 

44-  i 

23-5 

IO 

97-  » 

Si.  6 

70 

150.  i 

79.8 

30 

203.  I 

1  08.  o 

9° 

2^6.  I 

136.  i 

5' 

45.0 

23-9 

III 

98.  o 

52.  i 

171 

151.  o 

80.  3 

231 

204.  o 

1  08.  4 

291 

256.  g 

136.6 

52 

45-9 

24.4 

12 

98.9 

52.6 

72 

151.9 

80.  7 

32 

204.  8 

1  08.  9 

92 

257.8 

137.  i 

53 

46.  8 

24-9 

13 

99.8 

53-1 

73 

152.7 

81.2 

33 

205.  7 

109.4 

93 

258.7 

137-6 

54 

47-  7 

25.4 

'4 

loo.  7 

53-5 

74 

153-6 

81.7 

34 

206.  6 

109.9 

94 

259.  o 

138.0 

55 

48.  6 

25.8 

15 

101.  5 

54-0 

75 

154-5 

&2.2 

35 

207.  5 

1  10.  3 

95 

260.  5 

I38-5 

56 

49-4 

26.3 

16 

102.  4 

54-5 

76 

155-4 

82.  6 

36 

208.  4 

1  10.  8 

96 

261.  4 

139-  o 

57 

50-3 

:5.8 

17 

103.3 

54-  9 

77 

156-3 

83-1 

37 

209.  3 

111.3 

97 

262.  2 

139-  4 

58 

51.2 

27.  2 

18 

104.  2 

55-4 

78 

157.2 

83-6 

38 

210.  I 

in.  7 

98 

263.  i 

•39-9 

59 

52.1 

27.7 

19 

lOJ.  1 

55-9 

79 

158.0 

84.0 

39 

211.  O 

112.  2 

99 

264.  o 

140.  4 

60 

53-o 

28.  2 

20 

loo.  o 

5°-3 

80 

158.9 

84.5 

40 

211.  9 

112.  7 

300 

264.  9 

140.  8 

Dist. 

Dep. 

Lat. 

nist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat 

[For  62  Degrees. 

141 


DIFFERENCE.  OF  LATITUDE  AND  DEPARTURE  FOR  29°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.9 

0.  5 

6l 

53-4 

29.  6 

121 

105.8 

58.7 

181 

158.3 

87.8 

241 

210.  8 

116.8 

2 

'•  7 

I.  O 

6j> 

54-2 

30.1 

22 

106.  7 

59.1 

8= 

159.2 

88.2 

42 

211.  7 

"73 

3 

2.6 

'•5 

63 

55-  i 

3°-5 

23 

107.  6 

59-6 

83 

1  60.  I 

88.  7 

43 

212.  5 

117.8 

4 

3-  ^ 

1.9 

64 

56-  ° 

31.0 

24 

io3.  5 

60.  i 

84 

160.9 

89.2 

44 

213-4 

118.3 

5 

4-4 

2.4 

65 

56.9 

3'-S 

25 

"°9-3 

60.6 

f5 

161.8 

89.7 

45 

2«4-3 

118.  8 

6 

5.  2 

2.  9 

66 

57-  7 

32.0 

26 

IIO.  2 

61.  i 

86 

162.  7 

90.  2 

46 

215.2 

"9-3 

7 

6.  i 

3-4 

67 

50.  6 

32-5 

27 

III.  I 

61.6 

87 

163.6 

90.  7 

47 

216.  o 

119.7 

8 

7.0 

3-9 

68 

59-5 

33-  ° 

28 

112.  0 

62.  i 

88 

164.4 

91.1 

48 

216.  9 

1  2O.  2 

9 

7-9 

4-4 

69 

60.  3 

33-5 

29 

112.  8 

62.5 

89 

«65-3 

91.  6 

49 

217.8 

120.  7 

10 

8-7 

70 

61.2 

33-9 

30 

"3-7 

63.  o 

90 

166.2 

92.  i 

5° 

218.  7 

121.  2 

II 

9.6 

5-3 

71 

62.  i 

34-4 

13' 

114.6 

^3-5 

191 

167.  i 

92.  6 

251 

219.5 

I2I.7 

12 

10.5 

72 

63.  o 

34-9 

32 

115.4 

64.  o 

92 

167.9 

93-' 

52 

220.  4 

122.  2 

13 

11.4 

6-  3 

73 

63.8 

35-4 

33 

116.  3 

64.5 

93 

168.8 

93-  6 

53 

221.  3 

122.  7 

14 

12.  2 

6.  8 

74 

64.7 

35-9 

34 

117.  2 

65.  o 

54 

169.7 

94.1 

54 

222;  2 

I23.I 

15 

'3-  i 

7.3 

75 

65.6 

36.4 

35 

118.  i 

65.4 

95 

170.  6 

94-5 

55 

223.0 

123.  6 

16 

14.  o 

7-8 

76 

66.5 

36.8 

36 

118.9 

65-9 

96 

171.4 

95.0 

56 

223.  9 

124.  i 

17 

14.9 

8.2 

77 

67-3 

37-3 

37 

119.  8 

66.4 

97 

1/2.3 

95-5 

57 

224.8 

124.  6 

18 

*5-  7 

8.7 

78 

68.2 

37-8 

1  20.  7 

66.9 

98 

"73-2 

96.  o 

58 

225.7 

125.1 

'9 

1  6.  6 

9.2 

79 

69.  i 

38.3 

39 

121.  6 

67.4 

99 

174.0 

96-5 

59 

226.  5 

125.6 

20 

'7-5 

9-  7 

80 

70.  o 

38.8 

40 

122.  4 

67.9 

200 

'74-9 

97.0 

60 

227-4 

126.  i 

21 

18.4 

10.  2 

Si 

70.8 

39-3 

141 

123-3 

68.4 

201 

175.8 

97-4 

261 

228.3 

126.  5 

22 

19.2 

10.  7 

82 

71.  7 

•39-8 

42 

124.  2 

60.8 

C2 

176.7 

97-9 

62 

229.  2 

127.0 

23 

20.  I 

II.  2 

83 

72.6 

40.  2 

43 

125.  I 

69-3 

°3 

'77-5 

98-4 

63 

230.  o 

127.5 

24 

21.  O 

ii.  6 

84 

73-5 

40.  7 

44 

125.9 

69.8 

04 

178.4 

98.9 

64 

230.9 

128.0 

25 

21-9 

12.  I 

85 

74-3 

41.2 

45 

126.8 

7°-3 

°5 

179-3 

99-4 

65 

231.  8 

128.5 

26 

22.  7 

12.  6 

86 

75-2 

41.  7 

127.7 

70.8 

06 

180.2 

99-9 

66 

232.  6 

129.  o 

27 

23.  6 

I3.  I 

87 

76.1 

42.2 

47 

128.6 

7'-3 

07 

181.0 

100.  4 

67 

233-5 

129.4 

28 

24.5 

13.6 

88' 

77.0 

42-7 

48 

129.4 

71.8 

08 

181.9 

100.  8 

68 

234-4 

129.9 

29 

25.4 

14.  I 

89 

77.8 

43-1 

49 

•3°-3 

72.2 

09 

182.8 

101.3 

69 

235-3 

130.4 

3° 

20.  2 

H-5 

90 

78.7 

43-  6 

5° 

131.2 

72-7 

IO 

183.7 

101.8 

70 

236.  i 

1  30;  9 

3' 

27.1 

15.0 

9« 

79.6 

44-  ' 

'51 

132.  i 

73-2 

211 

184.5 

1  02.  3 

271 

237-0 

'3«-4 

32 

28.0 

'5-5 

.92 

80.5 

44-6 

52 

132-9 

73-7 

12 

185.  4 

102.  8 

72 

237-9 

«3'-9 

33 

28.9 

1  6.  o 

93 

81.3 

45-  I 

53 

'33-8 

74.2 

'3 

186.3 

103.  -5 

73 

238-8 

>32-4 

34 

29.  7 

16.5 

94 

82.2 

45-6 

54 

134-7 

74-7 

'4 

187.2 

'°3-  7 

74 

239.6 

132.8 

35 

30.  6 

17.0 

S3-' 

46.  i 

55 

135-6 

75-' 

'5 

1  88.  o 

104.  2 

75 

240.5 

133-3 

36 

3'-5 

'7-5 

96 

84.0 

46.5 

136.4 

75-6 

16 

188.9 

104.7 

76 

241.4 

133-8 

37 

32-4 

17.9 

97 

84.8 

47.0 

57 

'37-3 

76.1 

17 

189.  8 

105.  2 

77 

242-3 

134-3 

S8 

33-2 

1  8.  4 

98 

85.7 

47-5. 

58 

138.  2 

76.6 

18 

190.7 

105.7 

78 

243-' 

134.8 

39 

34-  i 

18.9 

99 

86.  6 

48.0 

59 

I39-I 

77-  1 

19 

191.5 

1  06.  2 

79 

244.0 

'35-3 

40 

35-  ° 

19.4 

loo 

87-  S 

48.5 

60 

139-9 

77-6 

20 

192.4 

106.  7 

80 

244.  -9 

"35-7 

41 

42 

35-9 
36-7 

19.9 

20.  4 

1OI 

02 

88.3 
89.2 

49.0 
49-5 

161 

62 

140.  8 
141.  7 

78.1 
78.5 

221 
22 

193-3 
194.2 

107.1 
107.  6 

281 

82 

245.8 
246.  6 

136.2 
136-7 

43 

37-6 

20.8 

°3 

90.  i 

49-9 

63 

142.  6 

79.0 

23 

195.0 

1  08.  i 

83 

247-5 

137-2 

44 
45 

38.5 
39.  4 

21.3 

21.  a 

04 
05 

91.  o 
91.8 

50.4 
50.9 

64 
65 

>43-4 
"44-3 

79-5 

bO.  O 

24 
25 

195.9 
196.8 

1  08.  6 
109.  i 

84 

248.4 
249-3 

'37-7 
138.2 

46 

40.  2 

22.  3 

06 

92.7 

51.4 

66 

145.2 

80.5 

26 

"97-7 

109.  6 

86 

250.  i 

138-7 

47 

41.  I 

22.8 

07 

93-6 

51.9 

67 

146.  i 

Si.o 

27 

198.5 

no.  i 

87 

251.0 

'39-  ' 

48 

42.  o 

23-3 

08 

94-5 

52.4 

68 

146.  9 

81.4 

28 

199.  4 

no.  5 

88 

251.9 

139.6 

49 

42.  9 

23-2 

09 

95-3 

52.8 

69 

147.8 

81.9 

29 

200.  3 

III.  O 

89 

252.8 

140.  i 

5° 

43-7 

24.2 

10 

96.2 

53-3 

7° 

148.  7 

82.4 

3° 

201.  2 

111.5 

90 

253-6 

140.  6 

51 

44-  6 

24.  7 

in 

97.1 

53-8 

171 

149.  6 

82.  9 

231 

202.  O 

I  12.  O 

291 

254-5 

141.  I 

52 

45-5 

25.2 

12 

98.0 

54-3 

72 

150.4 

83-4 

32 

2O2.  9 

II2.5 

92 

255-4 

141.  6 

53 

46.4 

25-  7 

'3 

98.8 

54-8 

73 

'5'-3 

83-9 

33 

203.8 

113.  o 

93 

256-3 

142.0 

54 

47.2 

20.  2 

14 

99-  7 

55-3 

74 

152,2 

84.  4 

34 

204.7 

"3-4 

94 

257.1 

142.5 

55 

48.1 

26.  7 

15 

100.  6 

75 

I53.  i 

84.8 

35 

205.5 

i  ''3-  9 

95 

258.0 

143-0 

56 

49-  ° 

27.  i 

16 

101.  5 

50!  2 

76 

153-9. 

85.3 

36 

rob.  A 

114.4 

96 

258.9 

'43-5 

57 

49-9 
50.  7 

27.6 
28.  I 

\l 

102.  3 
103.2 

56.7 
57-2 

77 
78 

154.8 
'55-7 

85.8 
86.3 

37 
38 

207.3 

208.  2 

114.9 
115.4 

97 
98 

259-8 
260.6 

144.0 
144.5 

59 

51.6 

28.6 

'9 

104.  i 

57-7 

79 

156.6 

86.8 

39 

209.  o 

"5-9 

99 

261.  5 

145.0 

DO 

52-5 

29.  I 

20 

105.  o 

58.2 

80 

I57.4 

87-3 

40 

209.9 

i  id.  4 

300 

262.4 

145.4 

Dlst. 

Dep. 

Lat. 

DU. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat 

[For  6  1  Degrees. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  30°. 

Dist 

L«t. 

Do,, 

Dl«t 

Ut 

Uep 

Di«t 

Lat. 

Dcp 

DM. 

I  at. 

Dep. 

DM. 

Lat 

Dep. 

1 

0.9 

o.  5 

61 

52.8 

3°-5 

121 

H>4.  8 

60  5 

iSl 

156.  8 

90.5 

241 

208.  7 

120.  5 

2 

1-7 

1.  O 

62 

53-7 

31.0 

22 

105.  7 

61.  o 

82 

157.6 

91.  o 

42 

209.  6 

121.  O 

3 

2.6 

'•5 

63 

54.6 

31-5 

23 

1  06.  5 

61.5 

83 

158.5 

91.5 

43 

210.  4 

I2I-5 

4 

3-5 

2.  0 

64 

55-  4 

32.  o 

24 

107.4 

02.  O 

84 

159-3 

92.  o 

44 

211.3 

122.  O 

5 

4-3 

*•  5 

65 

5°-  3 

32-5 

25 

108.  3 

62.5 

85 

l6o.  2 

92  5 

45 

212.  2 

122.5 

6 

5-2 

3-  ° 

66 

57-2 

33-° 

26 

109.  i 

63.  o 

86 

161.  i 

93-° 

4b 

213.  o 

123.  o 

7 

6.  i 

3-  5 

67 

58.  o 

33-  5 

27 

no.  c 

63.5 

87 

161.  9 

93-5 

47 

213-9 

123-5 

8 

6.  9 

4.0 

68 

58  a 

34-  o 

28 

no.  9 

64  o 

83 

162.  8 

94-0 

48 

214.  8 

124.  o 

9 

7-8 

4-  5 

69 

59.  S 

34-  5 

29 

111.7 

64.5 

89 

163-  7 

94-  5 

49 

215.  6 

124.  5 

10 

8-7 

7° 

60.  6 

35-0 

3° 

112.  6 

65.  o 

qo 

164.  5 

95.0 

50 

216.  5 

125.  o 

12 

9-5 
10.4 

5-5 
6.0 

72 

61.5 
62  4 

35-5 
36.  o 

131 
32 

"3-4 
H4-3 

65.5 

66.0 

191 

92 

165.4 
1  66.  3 

95-5 
90.  o 

251 
52 

217.4 
218.2 

•125-  5 
126.  o 

13 

"•3 

6.5 

73 

63.  2 

36.5 

33 

115.2 

66.  5 

93 

167.1 

96.5 

53 

219.  i 

126.5 

14 

12.  I 

7-o 

74 

64.I 

37-° 

34 

116.  o 

67.  o 

94 

168.0 

97-o 

54 

220.  o 

127.  o 

15 

13.0 

7-5 

75 

65  o 

37-5 

35 

1  16.  9 

67.5 

95 

1  68.  9 

97-5 

55 

220.  8 

127-5 

16 

13-9 

8.0 

76 

65  8 

38.  o 

36 

117.  8 

68.  o 

96 

169.  7 

98.  o 

221.  7 

128.0 

17 

I4.7 

8.5 

77 

66  7 

38-5 

37 

118.  6 

68.5 

97 

170.  6 

98.5 

57 

222.  6 

123.  5 

iS 

•5-6 

9.0 

78 

67-5 

39-  o 

38 

119.5 

69.  o 

9S 

171-5 

99.0 

58 

223.4 

129.  o 

19 

16.5 

9-5 

79 

68  4 

39-5 

39 

1  20.  4 

69.  5 

99 

i"2-3 

99-5 

59 

224-3 

129.  5 

20 

•7-3 

10.  o 

80 

^9-3 

40.  o 

40 

121.  2 

70.  o 

200 

173-2 

IOO.  O 

60 

225.  2 

130.  o 

21 

IS.  2 

10.5 

Si 

70  i 

40.5 

141 

122.  I 

70.5 

201 

174.  i 

ioo.  5 

261 

226.  o 

ijO-5 

22 

19.  I 

II    O 

82 

71.0 

41.0 

42 

123.  o 

71.0 

02 

174-9 

101.  o 

62 

226.  9 

131.  o 

23 

19.9 

11.5 

83 

71  9 

41-5 

43 

123.  8 

03 

175.8 

101.  5 

63 

227.  8 

I3I-5 

24 

20.  8 

12.  O 

84 

T2  7 

42.0 

44 

124-  7 

72.0 

04 

176.  7 

102.  O 

64 

228.6 

13=  o 

25 

21-7 

12-5 

85 

73  6 

42-5 

45 

125.6 

72-5 

05 

1/7-5 

1  02.  5 

65 

229.5 

132.5 

26 

22-5 

13.0 

86 

74-5 

43-  ° 

46 

126.4 

73-0 

06 

178.4 

103.  o 

66 

230-4 

133-0 

27 

-23-4 

'3-5 

87 

75  3 

43-5 

47 

127-3 

73-5 

07 

i79-3 

i°3-5 

67 

231.  2 

133.5 

28 

24.2 

14.  o 

00 

OO 

76  2 

44-  ° 

48 

128.  2 

74.0 

08 

1  80.  i 

104.  o 

68 

232.  I 

134-  0 

29 

25.1 

14.5 

89 

77-  i 

44-5 

49 

129.  o 

74-5 

09 

181.0 

104.  5 

69 

233-0 

134-5 

3° 

26.  o 

15.0 

90 

77-9 

45-0 

50 

129.  9 

75.0 

10 

181.  9 

105.  o 

7° 

233-8 

'35-o 

3i 

26.  8 

15-5 

91 

78.  8 

45-5 

151 

130.8 

75-5 

211 

182,  7 

i°5-5 

271 

234-  7 

135-5 

32 

27-7 

1  6.  o 

92 

79  7 

46.  o 

S2 

131.  6 

76.0 

12 

183.6 

1  06.  o 

72 

235-  ° 

136.  o 

33 

28.6 

16.5 

93 

80.  5 

46.5 

53 

132-5 

76-5 

13 

184.5 

io6p5 

73 

236.4 

136.  5 

34 

29.4 

17.0 

94 

Si  4 

47.0 

54 

133-4 

77.0 

185-3 

107.  o 

74 

237-3 

137-0 

35 

3°-3 

!7-5 

95 

82.3 

47-5 

55 

134-2 

77-5 

15 

186.2 

107-5 

75 

238.2 

137-5 

3° 

31-2 

18.  q 

96 

83.. 

48.  o 

56 

135-1 

78.0 

16 

187.  i 

1  08.  0 

230.  o 

,38.0 

37 

32.  o 

18.5 

97 

84.  o 

48.5 

57 

136.  o 

78.5 

17 

187.9 

1  08.  5 

77 

239-9 

138-5 

38 

32-9 

19.  o 

98 

84.9 

49-0 

58 

136.8 

79-o 

18 

iSS.  8 

109.  o 

78 

240.  8 

i39-o 

39 

33-8 

19-5 

99 

85.7 

49-5 

59 

137-7 

79-5 

'9 

189-7 

109.5 

79 

241.  6 

139-5 

40 

34-6 

20.  o 

loo 

£6.  6 

50.  o 

60 

138.6 

So.  o 

20 

190.5 

110.  0 

So 

242.  5 

140.  o 

41 

35-5 

20.5 

101 

87.5 

50-5 

161 

139-4 

So.  5 

221 

191.4 

no.  5 

281 

243-4 

140.5 

42 

36-4 

21.  0 

02 

88.3 

51.0 

62 

140.  3 

Si.o 

22 

192-3 

I1I.O 

82 

244.  2 

141.  o 

43 

37-2 

21-5 

°3 

89.2 

5i-5 

63 

141.  2 

81.5 

23 

193-  i 

in.  5 

83 

245.  i 

141.5 

44 

38-1 

22.  O 

04 

go.'i 

52.0 

64 

142.  o 

82.0 

24 

194.0 

112.  0 

84 

246.  o 

142.  o 

45 

39-o 

22-5 

o'5 

90.  9 

52.5 

65 

142.9 

82.5 

25 

194.9 

II2-5 

85 

246.8 

142.5 

46 

39-8 

23.0 

06 

91.8 

53-o 

66 

143.8 

83.0 

26 

195-7 

II3-0 

86 

247-  7 

143.0 

47 

40-  7 

23-5 

°7 

92-7 

53-5 

67 

144.6 

83-5 

27 

196.  6 

"3-5 

87 

248.5 

143-5 

48 

41.6 

24.  o 

08 

93-5 

54-o 

68 

145-5 

84.0 

28 

J97-5 

114.  o 

88 

249.4 

144.0 

49 

42.4 

24-5 

09 

94-4 

54-5 

69 

146.4 

84.5 

29 

198.3 

114.5 

89 

250.3 

144.  5 

5° 

43-3 

25-.  o 

10 

91-3 

55-o 

7° 

147.2 

85.0 

3° 

199-  2 

115.  o 

90 

251.1 

145.0 

5' 

44-2 

25.5 

III 

96.  i 

55-5 

171 

148.  I 

85-5 

231 

200.  I 

115.5 

291 

252.  o 

145-5 

52 

45-o 

26.  o 

12 

97.0 

56.  o 

72 

149.0 

86.0 

3- 

200.  9 

116.  o 

92 

252.9 

146.  o 

53 

45-9 

26.5 

13 

97-9 

56.5 

73 

149.8 

86.  5 

33 

201.8 

116.  5 

93 

253-7 

146.5 

54 

46.8 

27.0 

H 

98.7 

57-o 

74 

150.  7 

87.0 

34 

202.  6 

117.  o 

94 

254.6 

147-0 

55 

47-6 

27-5 

15 

99.6 

57-5 

75 

151.  6 

87-5 

35 

203-  5 

117-5 

95 

255-5 

147-5 

56 

48.5 

28.0 

1  6 

100.  5 

58.  o 

7° 

152.4 

88.0 

36 

204.4 

118.  o 

90 

256-3 

148.  o 

57 

49-4 

28.5 

17 

101.  3 

58.5 

77 

153-3 

88.  5 

37 

205.  2 

118.  5 

97 

257.2 

148.5 

58 

50.2 

29.  o 

18 

IO2.  2 

59.0 

78 

154.2 

89.  o 

38 

206.  I 

119.  o 

98 

258.  i 

149.0 

59 

51.1 

29-5 

19 

103.  I 

59-5 

79 

155.0 

89-5 

39 

207.  o 

119.  5 

99 

258.9 

149-5 

60 

52.0 

30.  o 

20 

103.9 

60.  o 

80 

155-9 

90.  o 

40 

207.8 

1  2O.  O 

300 

259.8 

150.  o 

Dist. 

Dep. 

Lat. 

DUt. 

Dep. 

Laf 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

[For  60  Degrees. 

143 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  31°. 

Dist. 

Lat. 

.Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep 

I 

0.9 

0.S 

61 

52-3 

31-4 

121 

I°3-7 

62.3 

iSl 

155.1 

93-  2 

24' 

206.  6 

124.  I 

2 

1-7 

I.  O 

62 

53-1 

3i-9 

22 

104.  6 

62.8 

82 

156.  o 

93-  7 

42 

207.4 

124.  6 

3 

2.6 

i-5 

63 

54-0 

32-4 

23 

105.4 

63-3 

83 

150.9 

94-  3 

43 

208.  3 

125.2 

4 

3-4 

2.  I 

64 

54-9 

33-o 

24 

106.  3 

63-  9 

84 

157-7 

94.8 

44 

209.  i 

125.  7 

5 

4-3 

2.6 

65 

55-7 

33-5 

25 

107.  i 

64.4 

85 

158.6 

95-3 

45 

210.  0 

126.  2 

6 

5-  ' 

3-  i 

66 

56.  6 

31-  ° 

26 

108.  o 

64-9 

86 

159-4 

95.8 

46 

210.  9 

126.  7 

7 

6.  o 

3-6 

67 

57-4 

34-5 

27 

1  08.  9 

65.4 

87 

160.3 

96.  3 

47 

211.  7 

127.2 

8 

6.9 

4-1 

68 

SS-3 

35-  ° 

28 

109.  7 

65.9 

88 

161.  i 

96.8 

48 

212.  6 

127.  7 

9 

7-7 

4.6 

69 

59-i 

35-5 

29 

no.  6 

66.4 

89 

162.  o 

97-3 

49 

213.4 

128.  2 

10 

8.6 

f..  2 

7° 

60.  o 

36.1 

3° 

III.  4 

67.  o 

90 

162.  9 

97-9 

50 

214.  3 

1  28.  S 

ii 

9.4 

5-7 

7' 

60.  9 

36.  6 

I31 

112.3 

67.5 

191 

i63-7 

98.  4 

251 

215.  i 

129.3 

12 

10.3 

6.2 

72 

61.7 

37-i 

32 

113.  i 

68.  o 

92 

164.  6 

98.9 

52 

216.  o 

129.8 

'3 

ii.  i 

6.7 

73 

62.6 

37-6 

33 

114.  o 

68.5 

93 

165.4 

99-4 

53 

216.  9 

130-3 

14 

12.  O 

7-2 

74 

63-4 

38.1 

34 

114.9 

69.  o 

94 

166.3 

99-9 

54 

217.  7 

130.  8 

'5 

12-9 

7-7 

75 

64-3 

38.6 

35 

115.7 

69.5 

95 

167.  i 

100.  4 

55 

210.  6 

I3I-3 

1  6 

13-7 

8.2 

76 

65.1 

39-  i 

36 

116.  6 

7<s.  o 

96 

168.  o 

100.  9 

56 

219.  4 

131.8 

«7 

14.  6 

8.8 

77 

66.0 

39-7 

37 

117.4 

70.  6 

97 

1  68.  9 

101.  5 

57 

220.  3 

i32-4 

18 

15.4 

9-3 

7» 

66.9 

40.  2 

38 

118.3 

71.1 

9S 

169.7 

102.  O 

58 

221.  I 

i32-9 

19 

16.3 

9.8 

79 

67.7 

40.  7 

39 

119.  i 

71.6 

99 

170.  6 

102.  5 

59 

222.  O 

•33-4 

20 

17.1 

10.3 

80 

68.6 

41.2 

40 

120.  0 

72-  i 

2CO 

171.4 

103.  o 

60 

222.  9 

133-9 

21 

18.  o 

10.  » 

Si 

69.4, 

-#•7 

141 

1  20.  9 

72.6 

201 

172-3 

103.5 

261 

223.  7 

'34-4 

22 

18.9 

ii-  3 

82 

70.3 

42.2 

42 

121.7 

73-1 

02 

173-  ' 

104.  o 

62 

224.  6 

134-9 

23 

'9-7 

ii.  8 

83 

71.1 

42.  7 

43 

122.  6 

73-  7 

03 

i/4-o 

104.  6 

63 

225.4 

135-5 

24 

•20.  6 

12.4 

84 

72.0 

43-3 

44 

123.4 

74-2 

04 

174.9 

105.  i 

64 

226.  3 

136.  o 

25 

26 

21.4 
22.3 

12.9 
13-4 

85 
86 

72.9 
73-7 

43-8 
44-3 

4I 
46 

124-3 
US-  I 

74-7 
75-2 

°5 
06 

i;5-  7 
176.6 

105.  6 
1  06.  i 

65 
66 

227.  i 
228.  o 

i36-5 
137-0 

27 

23.1 

'3-9 

87 

74.6 

44-8 

47 

126.  o 

75-7 

°7 

1/7-4 

106.  6 

67 

228.  9 

•37-5 

28 

24.0 

14-4 

88 

75-4 

45-3 

48 

126.  9 

76.2 

08 

1/8.3 

107.1 

68 

229-  7 

138.0 

29 

24.9 

14.9 

89 

76-3 

45-8 

49 

127.7 

76.7 

09 

179.  i 

107.  6 

69 

230.  6 

138-5 

3° 

25.7 

'5-5 

90 

77-  i 

46.4 

5° 

128.6 

77-3 

10 

i  So.  o 

108.  2 

7° 

23'-4 

139-  i 

3' 

26.6 

16.  o 

9i 

78.0 

46.9 

«5i 

129.4 

77-8 

211 

I  So.  9 

108.  7 

271 

232-3 

139.6 

32 

27.4 

16.5 

92 

78.9 

47-4 

S2 

i3°-3 

78-3 

12 

181.  7 

log.  2 

72 

233-1 

140.  i 

33 

28.3 

17.0 

93 

79-7 

47-9 

53 

131.1 

78.8 

13 

182.6 

109.7 

73 

234.0 

140.  6 

34 

29.  i 

'7-5 

94 

80.6 

48.4 

54 

132.  o 

79-3 

14 

183.4 

I  10.  2 

74 

234-9 

141.1 

35 

30.  o 

18.  o 

95 

81.4 

48-9 

55 

132-9 

79-8 

15 

184.3 

1  10.  7 

75 

235-7 

1-41.  6 

36 

30-9 

18.5 

96 

82.3 

49-4 

56 

133-7 

80.  3 

16 

185.  i 

III.  2 

76 

236.  6 

142.  2 

37 

3'-  7 

19.1 

97 

83-1 

50.  o 

57 

134.6 

80.9 

i? 

1  86.  o 

in.  8 

77 

237-4 

142.7 

38 

32-6 

19.  6 

98 

84.0 

5°-5 

58 

'35-4 

81.4 

18 

186.9 

II2.J 

78 

238-3 

143.2 

39 

33-4 

20.  i 

99 

84.9 

51.0 

59 

i36-3 

Si.  9 

19 

I8/.7 

I  12.  8 

79 

239.  i 

143-7 

40 

34-3 

20.  6 

loo 

85.7 

5'-5 

60 

137-  i 

82.4 

20 

iSS.  6 

"3-  3 

So 

240.  o 

144.2 

4' 

35-  ' 

21.  I 

101 

86.6 

52.0 

161 

138.0 

82.  9 

221 

i  S9.4 

113.  S 

281 

240.  9 

144-7 

42 

36.  o 

21.  6 

02 

87.4 

52-5 

62 

138.9 

83-4 

22 

19°.  3 

iM-3 

82 

241.  7 

145.2 

43 

36-9 

22.  I 

°3 

88.3 

53-o 

63 

139-7 

84.0 

23 

191.  i 

114.9 

83 

242.  6 

145.8 

44 

37-7 

22.7 

04 

89.  i 

53-6 

64 

140.  6 

84.5 

24 

192.  o 

115.4 

84 

243-4 

146.3 

45 
46 

38.6 
39-4 

23.2 
23-7 

°5 

06 

90.0 
90.9 

54.1 
54.6 

11 

141.4 
142.3 

85.0 

85.5 

25 

26 

192.9 
"93-7 

115.  9 
116.  4 

g 

244-  3 
245.  i 

146.8 
147-3 

47 

4°-3 

24.2 

°7 

9i-  7 

55-  i 

67 

143-  i 

86.0 

27 

194.6 

116.  9 

87 

246.  o 

147.8 

48 

41.1 

24.7 

08 

92.  6 

55-6 

68 

144.0 

86.  s 

28 

195-4 

117.4 

88 

246.9 

148.3 

49 

42.0 

25.2 

09 

93-4 

56., 

69 

144.9 

87.0 

29 

196.3 

117.9 

89 

247-  7 

148.8 

5° 

42.9 

25.8 

10 

94-3 

56.7 

70 

145-7 

87.6 

30 

197.  i 

118.  5 

90 

248.  6 

149.  4 

51 

43-7 

26.3 

in 

95-i 

57-2 

»7' 

146.  6 

SS.  i 

23' 

198.  o 

119.  o 

291 

249.4 

149.9 

52 

44-  6 

26.8 

12 

96.  o 

57-7 

72 

147.4 

88.6 

32 

198.9 

119.  5 

92 

250-3 

150.4 

53 

45-4 

27-3 

13 

96.9 

58.2 

73 

148.3 

89.1 

33 

199-  7 

120.  0 

93 

251.2 

150-9 

54 

46-3 

27.8 

'4 

97-  7 

58.7 

74 

149.  i 

89.6 

34 

200.  6 

120.  5 

94 

252.  o 

151.4 

55 

47.1 

28.3 

15 

98.6 

59-2 

75 

150.  o 

90.  i 

55 

201.  4 

121.  0 

95 

252.9 

151.9 

56 

48.0 

28.8 

16 

99-4 

59-7 

76 

150.9 

90.  b 

36 

202.3 

121.  5 

96 

253-  7 

152.5 

57 

48.9 

29.4 

17 

100.  3 

60.3 

77 

151.7 

91.2 

37 

203.  I 

122.  I 

97 

254.6 

153.0 

58 

49-7 

29.9 

18 

IOI.  I 

60.8 

78 

152.  6 

91.7 

38 

204,  o 

122.  6 

98 

255-4 

153-5 

59 

50.  6 

3°-4 

19 

102.  O 

61.3 

79 

153-4 

92.  2 

39 

204.9 

123.  I 

99 

256-3 

154.0 

60 

51.4 

3°-9 

20 

102.  9 

61.8 

So 

154-3 

92.7 

4° 

205.  7 

123.6 

300 

257.  i 

154-5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

[For  59  Degrees. 

144 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  32°. 

Dlst 

I-at 

Dep. 

Dlst 

Lit 

Dep. 

Dlst 

Lat 

Dep. 

Dlst 

Lit 

Dep. 

DIM. 

Lat 

Dop. 

I 

0.8 

0.  5 

6l 

5'-  7 

32-  3 

121 

102.  6 

64.  I 

i  Si 

'53-5 

95-  9 

241 

204.  4 

127.7 

2 

'•7 

I.  1 

62 

52.6 

32-9 

22 

103.  5 

64.  7 

82 

'54-3 

96.  4 

42 

205.  2 

128.  2 

3 

2-5 

1.6 

63 

53-4 

33-4 

23 

'°4-  3 

65.2 

83 

155.2 

97.0 

43 

206.  I 

128.8 

4 

3-4 

2.  I 

64 

54-3 

3J-  9 

24 

105.  2 

65-7 

84 

156.  o 

97-5 

44 

206.  9 

':9-3 

5 

4-2 

2.6 

65 

55-  ' 

34-4 

25 

106.  o 

66.2 

85 

156.9 

98.  o 

45 

207.8 

129.8 

5 

5-  ' 

3-2 

66 

56.  o 

35-o 

2& 

1  06.  9 

66.  8 

86 

'57  7 

98.  6 

46 

208.  6 

130.4 

7 

5-9 

3-7 

67 

56.8 

35-5 

27 

107.  7 

67.3 

87 

158.  6 

99-  ' 

47 

209.  5 

130.9 

8 

6.8 

4.2 

68 

57-  7 

36.  o 

28 

108.  6 

67.8 

88 

159.  4 

99.  6 

48 

210.  3 

131.4 

9 

7.6 

4.8 

69 

58-5 

36.  6 

29 

109.4 

68.4 

89 

160.  3 

IOO.  2 

49 

211.  2 

131.9 

10 

8-5 

5-3 

7° 

59-4 

37-' 

3° 

no.  2 

68.9 

90 

161    i 

loo.  7 

5° 

212.  O 

•32-5 

II 

9-3 

5.  8 

7' 

60.  2 

37-6 

'3' 

in.  i 

69.  4 

191 

Ib2    O 

IOI.  2 

251 

212.  9 

133.  o 

12 

10.  2 

6.4 

72 

61.  i 

32 

in.  9 

69.  9 

92 

162.  8 

loi.  7 

52 

213.  7 

'33-5 

'3 

II.  0 

6.9 

73 

61.9 

3S.7 

33 

112.  8 

70.5 

93 

163.  7 

102.  i 

53 

214.  6 

'34-  ' 

14 

II.9 

7-4 

74 

62.  8 

39-2 

34 

113.  6 

71  o 

94 

'64-  5 

102    8 

54 

215.4 

'34-6 

15 

1  6 

12.7 
'3-6 

7-9 
8-5 

75 
76 

63.  6 
64.5 

39-  7 
40.  3 

9 

"4-  5 
115.3 

7'-5 

72.  i 

9 

165.  4 
166.  2 

I03-  3 
103.  9 

55 

216.3 
217  i 

'35-' 
'35-7 

'7 

'4-4 

9.0 

77 

65.3 

40.8 

37 

116.  2 

72.6 

97 

167.  i 

104.  4 

57 

217.0 

136.  2 

18 

"5-3 

9-5 

66.  i 

4'-3 

38 

117.  o 

73-  ' 

98 

167  9 

104.  9 

58 

218.  § 

'36-7 

>9 

1  6.  i 

10.  I 

79 

67.  o 

41.9 

39 

"7-9 

73-  7 

99 

168.  8 

105.  5 

59 

219.  6 

'37-  2 

20 

17.0 

10.  6 

80 

67.8 

42.  4 

4° 

118.  7 

74-2 

200 

169.  6 

106.  o 

60 

220.  5 

137.8 

21 

17.8 

11.  i 

81 

68.  7 

42-9 

141 

119.  6 

74-  7 

201 

170.  5 

106.  5 

261 

221.3 

•38-3 

22 

18.7 

11.7 

82 

69.  5 

43-5 

42 

120.  4 

75-2 

02 

'7'-3 

107  o 

62 

222.  2 

138.8 

23 

'9-5 

12.  2 

83 

TO-  4 

^^.  o 

43 

121.3 

-i'8 

03 

172.  2 

107.  6 

63 

223.  o 

'39-  4 

24 

20.4 

12.7 

84 

7'.2 

44-5 

44 

122.  I 

04 

'73-0 

108.  i 

64 

223.9 

'39-9 

25 

21.  2 

'3-2 

85 

72.  i 

45-  ° 

45 

123.  o 

76.  8 

05 

'73-8 

1  08.  6 

65 

224.  7 

140.  4 

20 

22.  O 

13.8 

86 

72.9 

45.  6 

46 

123.  8 

77-4 

06 

'74-  7 

109.  2 

66 

225.  6 

141.  o 

27 

22.  9 

'4-  3 

87 

73-8 

46.  i 

47 

124.  7 

77-9 

°z 

'75-5 

109.  7 

67 

226.  4 

141.5 

28 

23-  7 

14-8 

88 

74-6 

46.6 

48 

I25-5 

78.4 

08 

176.  4 

I  IO.  2 

68 

227-  3 

142.  o 

29 

24.  6 

15.4 

89 

75-5 

47.2 

49 

126.4 

79-o 

09 

177.2 

1  10.  8 

69 

228.  i 

142.  5 

3° 

25.4 

15.9 

90 

76.3 

47-7 

5° 

127.  2 

79-5 

IO 

178.  i 

111.3 

7° 

229.  o 

143.  i 

3' 

26.  3 

16.  4 

9' 

77-2 

48.  2 

151 

128.  I 

So.  o 

211 

178.9 

in.  8 

271 

229.  8 

143.6 

32 

27.  I 

17.0 

92 

78.0 

48.  8 

52 

128.  9 

80.5 

12 

179.8 

112.  3 

72 

230.  7 

144.  i 

33 

28.0 

'7-5 

93 

78.9 

49-  3 

53 

129.  8 

81.  i 

'3 

1  80.  6 

112.  9 

73 

23'-  5 

'44-  7 

34 

28.8 

18.  o 

94 

79-  7 

49.  8 

54 

130.  6 

81.6 

'4 

181.  5 

"3-4 

74 

232  4 

145.  2 

i 

29.7 

3°-5 

18.5 
19.  I 

9 

80.6 
81.4 

5°-3 
50.  9 

55 
5° 

131.  4 
'32-3 

82.  i 
82.7 

15 

1  6 

182.  3 
183.  2 

113.  9 
"4-  5 

9 

233-2 
234.1 

'45-  7 
146.3 

37 

3'-4 

19.  6 

97 

82.3 

51.4 

57 

'33-  ' 

83.2 

'7 

184.  o 

115.0 

77 

234.9 

146.8 

38 

32-2 

20.  i 

98 

83-' 

5'-  9 

58 

'34-0 

83-7 

18 

184.9 

"5-5 

78 

235-8 

147-3 

39 

33-  ' 

20.  7 

99 

84.  o 

52-5 

59 

'34-8 

84.3 

'9 

185.7 

79 

236.  6 

147.8 

40 

33-9 

21.  2 

IOO 

84.8 

53-0 

60 

'35-7 

84.8 

20 

1  86.  6 

116.  b 

80 

237-5 

148.4 

4' 

34-8" 

2'-7 

IOI 

85.7 

53-5 

161 

136-5 

85-3, 

221 

187.  4 

117.  I 

281 

238-3 

148.9 

42 

35-6 

22.  3 

02 

86.5 

54-  ' 

62 

'37-4 

85.  § 

22 

188.3 

1  17.  6 

82 

239-  ' 

149.4 

43 

36.5 

22.  8 

°3 

87-3 

54-6 

63 

138.  2 

86.4 

23 

189.  i 

I  I  8.  2 

83 

240.  o 

150.  o 

44 

37-  3 

23-3 

04 

88.2 

55-  ' 

64 

'39-  ' 

86.9 

24 

190.  o 

118.  7 

84 

240.  8 

150.5 

45 

38/2 

23-8 

89.  o 

139.9 

87.4 

2( 

190.  8 

119.  2 

85 

241.7 

151.  o 

46 

39-0 

24.4 

00 

89-9 

56.  2 

66 

140.  8 

88.0 

26 

191.  7 

119.  8 

86 

242.  5 

151.  6 

47 

39-9 

24.9 

07 

90.  7 

56.7 

67 

141.  6 

88.5 

27 

192.5 

120.  3 

87 

243-  4 

152.1 

48 

4°-  7 

25.4 

08 

91.  6 

57-2 

68 

142.5 

89.0 

28 

'93-  4 

120.  8 

88 

244-  2 

152.  6 

49 

41.6 

26.  o 

09 

92.4 

57-8 

69 

'43-3 

89.6 

29 

'94-  2 

121.  4 

89 

245-  ' 

'53-  > 

5° 

42.4 

26.5 

10 

93-3 

58.  3 

70 

144.  2 

90.  i 

3° 

195.  i 

121.  9 

90 

245-9 

'53-  7 

5' 

43-3 

27.0 

III 

94-  ' 

58.  8 

'7' 

145.0 

90.  6 

23' 

195.9 

122.4 

291 

246.8 

154-2- 

S2 

44-  ' 

27.  6 

12 

95.0 

59-4 

72 

'45-  9 

91.1 

32 

196.  7 

122.  9 

92 

247.6 

154-7 

S3 

44-  9 

28  i 

'3 

95.8 

59-9 

73 

146.7 

91.7 

33 

197.6 

'23-5 

93 

248-5 

'55-3 

54 
55 

45.8 
46.6 

28.  6 
29.  i 

'4 
15 

96.  7 
97-5 

60.4 
60.  9 

74 

147-6 
148.4 

92.  2 
92.7 

34 
35 

198.4 
'99-  3 

124.  o 
124.  5 

94 
95 

249-  3 

250.  2 

155.8 

'56-  3 

5° 

47-  5 

29.  7 

16 

98-4 

61.5 

7° 

'49-  3 

93-3 

36 

200.  i 

125.  1 

96 

251.0 

156.9 

57 

48-  3 

30.2 

'7 

99.  2 

62.  o 

77 

150.  i 

93-8 

37 

201    O 

125.  6 

97 

251.9 

'57-4 

58 

49-  2 

3°-7 

18 

IOO.   I 

62.5 

78 

151.  o 

94-3 

38 

201.8 

126.  I 

98 

252.7 

'57-9 

59 

50.  o 

31.  3 

'9 

100.  o 

63.' 

Z9 

151.  8 

94-9 

39 

202.  7 

r2b.  7 

99 

253.6 

158.4 

BO 

50.9 

3'.8 

20 

lol.  8 

63.6 

So 

152.  6 

95-4 

40 

203.5 

127.2 

300 

254.4 

159.0 

Dbt 

Dep, 

Lat 

Dlst 

Dep. 

Let 

Dikt 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dlst 

Dep. 

I  ^t 

[For  58  Degrees.' 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  33°. 

Dlst 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

I 

0.8 

0-5 

61 

51.2 

33-2 

121 

101.  5 

65.9 

181 

151.  8 

98.6 

241 

202.  1 

I3L3 

2 

i.  7 

I.  I 

62 

52.0 

33-8 

22 

102.3 

66.4 

82 

152.  6 

99-1 

42 

•203.  o 

131.8 

3 

2-5 

1.6 

63 

52.8 

34-3 

*3 

103.  2 

67.  o 

83 

153-5 

99-7 

43 

203.8 

132.3 

4 

3-4 

2.2 

64 

53-7 

34-9 

24 

IO4.O 

67.5 

84 

154-3 

ipo.  2 

44 

204.  6 

132.9 

5 

4-2 

2-7 

65 

54-5 

35-4 

25 

104.8 

68.1 

85 

155.2 

loo.  8 

45 

205-5 

133-4 

6 

5-o 

3-3 

66 

55-4 

35-9 

26 

105.7 

68.6 

So 

156.  o 

101.3 

46 

206.3 

134.0 

7 

5-9 

3-8 

6l 

56.  2 

36-5 

27 

106.  5 

69.  2 

87 

156.8 

101.  8 

47 

207.  2 

134-5 

8 

6-7 

4-4 

68 

57-o 

37-o 

28 

107.  3 

69.7 

88 

157-7 

102.  4 

48 

208.  o 

I35-I 

9 

10 

£5 

4-9 

5-4 

69 
70 

57-9 
58.7 

37-6 

29 
30 

108.2 
109.  o 

70-3 
70.8 

89 
90 

158.5 
159-3 

102.  9 

49 

208.8 
209.7 

135-6 

136.  2 

II 

9-2 

6.0 

71 

59-5 

3»-7 

131 

109.9 

71-3 

191 

lt>0.  2 

104.  o 

251 

210.  5 

136-7 

12 

10.  I 

6-5 

72 

60.4 

39-2 

32 

no.  7 

71.9 

92 

161.  o 

104.6 

S2 

211.  3 

137-2 

13 

10.9 

73 

61.2 

39-8 

33 

111.5 

72-4 

93 

161.9 

105.  1 

53 

212.  2 

137-8 

14 

ii.  2 

l'6 

74 

62.1 

40-3 

34 

112.4 

73-o 

94 

162.  7 

105-7 

54 

213.0 

138.3 

15 

12.6 

8.2 

75 

62.9 

40.  8 

113-2 

73-5 

'63-S 

1  06.  2 

55 

213.  9 

138.9 

1,6 

13-4 

8-7 

76 

63-7 

41'.  4 

3° 

114.1 

74-1 

96 

164.4 

106.  7 

S6 

214.7 

139-4 

17 

14-3 

9-3 

77 

64.6 

41.9 

37 

114.9 

74-6 

97 

165.3 

107-3 

57 

215-5 

140.0 

IS 

15.1 

9-8 

78 

65.4 

42.5 

38 

115.7 

75-2 

98 

1  66.  I 

107.8 

5« 

216.4 

140.5 

19 

20 

15-9 
16.8 

10.3 
ro.  9 

e 

66.3 
67.1 

43-  P 
43-6 

39 
40 

lib,  6 

117.4 

9.1 

99 

200 

166.9 
167.7 

108.4 
108.9 

217.  2 
2I&  I 

141.  I 

141.  6 

21 

17.6 

11.4 

81 

67.9 

44-  i 

141 

118.3 

76.  8~ 

201 

168.  6 

109.5 

261 

218.  9 

142.  2 

22 

18.5 

12.  O 

82 

68.8 

44-  7 

42 

119.  i 

77-3 

O2 

169.4 

IIO.  0 

62 

219.7 

142.7 

23 

19-3 

12-5 

83 

69.6 

45-2 

43 

119.9 

77-9 

03 

I70-3 

no.  6 

63 

220.  6 

143-  * 

24 

20.  I 

13-  I 

84 

70.4 

45-7 

44 

1  20.  8 

78.4 

04 

171.1 

ill.  1 

64 

221.4 

14^.8 

% 

21.0 
21.8 

13-6 

14.  2 

II 

71-3 
72.1 

46-3, 
46.8 

42 
46 

121.  6 

122.4 

79-o 
79-5 

05 
06 

171.9 

172.  2 

111.7 

112.  2 

s 

222.  2 
223.  I 

144-3 
144-9 

27 

22.6 

14-7 

87 

73-o 

47-4 

47 

123-3 

80.  i 

07 

173-6 

112.  7 

67 

223.0 

145.4 

29 

23-5 

15-2 

88 

73-8 

47-9 

4 

124.  i 

80.6 

08 

174.4 

113-3 

68 

224.8 

146.  o 

29 

24-3 

15-8 

89 

74-6 

48.5 

49 

125.0 

81.2 

09 

175-3 

II3-8 

69 

225.  6 

146.5 

30 

25.  2 

I6.3 

90 

75-5 

49-0 

5° 

125.8 

81.7 

10 

176.  I 

II4.4 

70 

226.4 

147-  ' 

32 

26.0 
26.8 

16.9 

17.4 

92 

76-3 
77-2 

49-6 
50.1 

151 

52 

126.6 
127-5 

82.2 
82.8 

211 

12 

177.0 
177,8 

II4.9 
II5.5 

271 

72 

327.3 
228.  i 

147.6 
148.  1 

33 

27-7 

18.0 

93 

78.0 

50.7 

53 

128.3 

83-3 

13 

178.6 

1  1  6.  o 

73 

229.0 

148.7 

34 

28.5 

18.5 

94 

78.8 

51-2 

54 

129.  2 

83-9 

14 

179-5 

116.6 

74 

329.  8 

149.2 

29-4 
30.2 

19.6 

9 

80.5 

Si-7 
52.3 

55 
S6 

130.0 
130.8 

84.4 
85.0 

3 

'180.3 

181.  2 

117.1 
117.  6 

75 
76 

230.  6 
231-5 

149.8 
150-3 

3Z 

31.0 

20.2 

97 

81.4 

52-8 

57 

131.7 

85.5 

17 

182.0 

118.2 

77 

232-3 

150.9 

3§ 

31.9 

20.  7 

98 

82.2 

53-4 

58 

I32-5 

86.  i 

18 

182.8 

118.  7 

78 

233-2 

151.4 

39 
40 

32-7 

33-5 

21.  2 
21.8 

99 

IOO 

83.0 

53-9 

'54-5 

£ 

133-3 
134-2 

86.6 
87.1 

19 

20 

183.7 
184.5 

"9-3 
119.8 

g 

234-0 
234.8 

152.0 

152.5 

41 

34-4 

22.  3 

101 

84-7 

55-0 

161 

135-0 

87.7 

221 

185.3 

1  20.  4 

281 

235-7 

153-0 

42 

35-2 

22.9 

02 

85-5 

55-6 

62 

135-9 

88.2 

22 

186.2 

120.  9 

83 

236-5 

153-  6. 

43 

36-1 

23-4 

03 

86.4 

56.1 

63 

88.8 

23 

187.0 

121.5 

83 

237-3 

I54-I 

44 

36-9 

24.0 

04 

87.2 

56.6 

64 

137-5 

89-3 

24 

187.9 

122.  0 

84 

238.2 

154-7 

45 

37,-  7 

24.  5 

88.1 

57-2 

65 

138.4 

89-9 

25 

188.7 

122.5 

85 

239.0 

If?.  2 

46 

38.6 

25-1 

oo 

88.9 

57-7 

66 

139.2 

90.4 

26 

189.5 

I23-I 

•So 

239-9 

155-8 

47 

39-4 

25.6 

07 

89.7 

58-3, 

67 

140.  I 

91.0 

27 

190.4 

123.6 

£7 

240-7 

156.3 

48 

4°-  3 

26.  i 

OB 

90-.  6 

58.8 

68 

140.9 

91.5 

28 

191.  2 

124.  2 

£3 

441.5 

I£5.9 

49 

41.  i 

26.7 

09 

91.4 

59-4 

69 

141.  7 

92.  o 

29 

192.  I 

124.7 

89 

242.4 

157-4 

50 

41.9 

27.2 

10 

92-3 

59-9 

70 

142.  6 

92.  6 

3° 

192.9 

125-3 

CO 

243.2 

157-9 

•Si 

42.8 

27.8 

III 

93-1 

60.5 

171 

143-4 

93-1 

231 

193-7 

125.8 

391 

244-1 

158.5 

52 

43-6 

28.3 

12 

93-9 

61.  o 

72 

144-3 

93-7 

194.6 

126.  4 

92 

244.9 

IS9-0 

53 

44-4 

28.9 

13 

94-8 

61.5 

73 

145.1 

94-2 

33 

195.4 

126.9 

93 

245-7 

159.  6 

54 

45-3 

29-4 

14 

95-6 

62.  I 

74 

J45-9 

94-8 

34 

196.  2 

127.  4 

94 

346.  6 

160.  i 

55 

46.1 

30.  o 

15 

96.4 

62.6 

75 

146.8 

95-3 

35 

197.  I 

128.0 

95 

247-4 

160.  7 

56 

47-o 

30-5 

16 

97-3 

63.  2 

76 

147.6 

95-9 

36 

197.9 

128.5 

96 

248.  2 

iSl.  2 

•57 

47.8 

31.0 

17 

98.1 

63-7 

77 

148.4 

96.4 

37 

198.8 

129.  I 

97 

»49-  I 

161.  8 

S8 

48.6 

31-6 

IB 

99.0 

64-3 

78 

149-3 

96.9 

38 

199.6 

129.  6 

98 

249.0 

162.3 

59 

49-5 

32.1 

.19 

99-8 

64.8 

150.  i 

97-5 

39 

200.  4 

130.  2 

99 

250.  8 

162.8 

6q 

50-3 

* 

32-7 

2O 

joo.  6 

65.4 

to 

151.0 

98.0 

40 

sol.  3 

130-  7 

300 

251.6 

163.4 

Dlst. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dlst 

Dep. 

Lat 

[For  57  Degrees. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  34°. 

Dist. 

Lai. 

Dcp. 

Pist. 

Lit. 

Dep. 

Dist. 

Lat. 

Dcp. 

Disl. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

50.6 

34-  « 

121 

IOO.  3 

67-7 

iSi 

150.  I 

IOI.  2 

24' 

199.8 

'34-8 

2 

1-7 

I.  I 

62 

51.4 

34-7 

22 

IOI.  I 

68.  2 

82 

150.9 

IOI.8 

42 

2OO.  6 

'35-3 

3 

2.5 

i-7 

63 

52.2 

35-2 

23 

102.0 

68.  8 

83 

15I.7 

102.  3 

43 

201.  5 

135-9 

4 

3-3 

2.  2 

64 

53-1 

35-8 

24 

102.8 

69-3 

84 

'52-5 

102.9 

44 

2O2.  3 

136.  4 

5 

4-  i 

2.8 

65 

53-9 

36-3 

25 

103.  6 

69.  9 

85 

'53-4 

l°3-5 

45 

203.  1 

'37-o 

6 

5.0 

3-4 

66 

54-7 

36-9 

26 

104.5 

70.5 

86 

154.2 

104.  o 

46 

203.9 

'37-6 

7 

5-8 

3-9 

67 

55-5 

37-5 

27 

i°5-3 

71.0 

87 

155.0 

104.  6 

47 

204.  8 

138.  i 

8 

6.6 

4-5 

68 

56.4 

38-0 

28 

106.  i 

71-6 

88 

'55-9 

105.  i 

48 

205.  6 

138-7 

9 

7-5 

5.0 

69 

57-2 

38.6 

29 

106.  9 

72.  i 

89 

156.7 

105.7 

49 

206.  4 

139.2 

10 

8:3 

5.6 

70 

58.0 

39-  I 

3° 

107.8 

72.7 

90 

"57-5 

1  06.  2 

5° 

207.3 

'39-8 

II 

9-1 

6.2 

7> 

5s-9 

39-7 

13' 

loS.  6 

73-3 

191 

'5s-  3 

106.8 

251 

208.  i 

140.4 

12 

9-9 

6.7 

72 

59-7 

4°-3 

32 

109.4 

73-8 

92 

159.2 

107.4 

S2 

208.  9 

140.9 

'3 

10.8 

7-3 

73 

60.5 

40.  8 

33 

no.  3 

74-4 

93 

1  60.  O 

107.9 

53 

209.7 

141.5 

«4 

11.  6 

7-8 

74 

61-3 

41.4 

34 

in.  i 

74-9 

94 

160.8 

108.5 

54 

2IO.  6 

142.  o 

'5 

12.4 

8.4 

75 

62.2 

41.9 

35 

111.9 

75-5 

95 

161.  7 

lOg.O 

55 

211.  4 

142.  6 

16 

'3-3 

8.9 

76 

63.  o 

42.5 

36 

112.7 

76.1 

96 

162.  5 

109.  6 

56 

212.  2 

143.2 

'7 

14.1 

.9-5 

77 

63.8 

43-  > 

37 

113.  6 

76.6 

97 

>63-3 

no.  2 

57 

2I3.I 

•43  7 

18 

14.9 

10.  I 

78 

64.  7 

43-  6 

38 

114.4 

77-2 

98 

164.  i 

1  10.  7 

58 

213-9 

144-3 

19 

15.8 

10.  6 

79 

65.5 

.44-2 

39 

115.2 

77-7 

99 

165.  o 

111.3 

59 

214.  7 

144.8 

20 

1  6.  6 

II.  2 

So 

66.3 

44-7 

40 

1  16.  i 

78.3 

200 

165.8 

in.  8 

60 

2'5-5 

145.4 

21 

17.4 

ii.  7 

81 

67.2 

45-3 

141 

116.  9 

78.8 

201 

166.6 

112.  4 

261 

216.  4 

'45-9 

22 

18.2 

12.3 

82 

68.0 

45-9 

42 

117.  7 

79-4 

O2 

167.5 

113.0 

62 

217.2 

146.5 

23 

19-1 

12.9 

83 

68.  8 

46.4 

43 

118.  6 

80.0 

°3 

168.3 

"3-5 

63 

215.0 

147.  I 

24 

19.9 

13-4 

84 

69.6 

47.0 

44 

119.4 

80.5 

04 

169.  I 

114.  i 

64 

218.9 

147.6 

25 

20.7 

14.  o 

85 

70.5 

47-5 

45 

120.  2 

81.  i 

°5 

170.0 

114.  6 

65 

219.7 

148.  2 

26 

21.6 

14.5 

86 

7'-3 

48.  i 

46 

121.  O 

81.6 

06 

170.8 

115.2 

66 

22O.  5 

148.7 

27 

22.4 

15.1 

87 

72.1 

48.6 

47 

121-9 

82.2 

07 

171.6 

115.8 

67 

221.  4 

'49-3 

28 

23.2 

15-7 

88 

73-0 

49-2 

48 

122.  7 

82.8 

08 

172.4 

116.3 

68 

222.2 

149.9 

29 

24.  o 

16.  2 

89 

73-8 

49,8 

49 

123-5 

83-3 

09 

173-3 

116.9 

69 

223.  o 

150.4 

3° 

24.9 

16.  8 

90 

74.6 

5°-3 

5° 

124.4 

83-9 

IO 

174.  I 

117.4 

70 

223.8 

151.0 

3' 

25.7 

'7-3 

91" 

75-4 

50.9 

'5' 

125.2 

84.4 

211 

174.9 

118.0 

271 

224.  7 

'5>-5 

32 

26.5 

17.9 

92 

7°-3 

51.4 

52 

126.  o 

85.0 

12 

175-8 

118.5 

72 

225-5 

152.1 

33 

27.4 

18.5 

93 

77-  > 

52.0 

53 

126.8 

85.6 

'3 

176.6 

119.  l 

73 

226.3 

152.7 

34 

28.2 

19.  o 

94 

77-9 

52.6 

54 

127.7 

86.  i 

14 

177-4 

119.7 

74 

227.2 

153-2 

35 

29.0 

19.  6 

95 

78.8 

S3-' 

55 

128.5 

86.  7 

15 

178.2 

120.2 

75 

228.0 

'53-8 

36 

29.8 

20.  i 

96 

79.6 

53-7 

56 

J-9-3 

87.2 

16 

179.1 

120.8 

76 

228.8 

154-3 

37 

3°-7 

20.7 

97 

80.4 

54.2 

57 

•130.  2 

87.8 

17 

179.9 

I2I-3 

77 

22O.6 

'54-9 

3» 

3'-5 

21.  2 

98 

Si.  2 

54.8 

58 

131.  o 

88.4 

18 

1  80.  7 

I2I-9 

78 

230-5 

»55-  5 

39 

32-3 

21.8 

99 

82.1 

55-4 

59 

I3I.-8 

88.9 

'9 

181.6 

122.  5 

79 

23'-  3 

156.0 

40 

33-2 

22-4 

IOO 

82.  9 

55-9 

60 

132.  6 

89.5 

20 

182.4 

123.  o 

80 

232.  1 

156.6 

4' 

34-o 

22.  9 

IOI 

83-7 

56-5 

161 

'33-5 

90.  o 

221 

183.2 

123.  6 

281 

233.0 

157.1 

42 

34-8 

23-5 

02 

84.6 

57-o 

62 

'34-3 

90.  6 

22 

184.0 

124.  I 

82 

233.8 

'57-7 

43 

35-6 

24.  o 

03 

8.5-4 

57-6 

63 

'35-  ' 

91.1 

23 

184.9 

124.7 

83 

234.6 

I5?-i 

44 

36-5 

24.  6 

04 

86.2 

58.2 

64 

136.0 

91.7 

24 

185.7 

125-3 

84 

235.4 

158.8 

45 

37-3 

25-2 

05 

87.0 

58.7 

65 

136.8 

92-3 

25 

186.5 

125.8 

85 

236.3 

159.4 

46 

38-1 

25.7 

06 

87-9 

59-3 

66 

137.6' 

92.8 

26 

187.4 

126.4 

86 

237.1 

159.9 

47 

39-o 

26.3 

07 

88.  7 

59-8 

67 

138.4 

93-4 

27 

188.2 

126.  9 

87 

237.9 

160.  5 

48 

39-8 

26.8 

08 

89-5 

60.4 

68 

'39-3 

93-9 

28 

189.0 

127.5 

88 

238.8 

161.0 

49 

40.  6 

27.4 

09 

90.4 

61.  o 

69 

140.  i 

94-5 

29 

189.8 

128.  i 

89 

239.6 

161.6 

5° 

41.5 

28.0 

10 

91.  2 

6i-5 

70 

140.9 

9S-I 

3° 

190.  7 

128.6 

90 

240.4 

162.  2 

5' 

42-3 

2b.S 

III 

92.  o 

02.  I 

'7" 

141-8 

95-6 

231 

191-5 

129.2 

291 

241.  2 

162.  7 

52 

43-1 

29.  I 

12 

92.9 

62.6 

72 

142.  6 

95.  2 

32 

192.3 

129.7 

92 

242.  I 

163.3 

S3 

43-9 

29.  6 

'3 

93-7 

63.  2 

73 

143-4 

96-  7 

33 

193-2 

'3°-3 

93 

i42.9 

163.8 

54 

44.8 

30.2 

14 

94-5 

63.7 

74 

144-3 

97-3 

34 

194.0 

130.9 

94 

243-7 

164.4 

55 

45.6 

30.8 

15 

95-3 

64.3 

75 

145.  i 

97-9 

35 

194.8 

131-4 

95 

244.6 

165.0 

56 

46.4 

3'-  3 

16 

96.  2 

64.9 

76 

145.9 

98.4 

36 

195-7 

132.0 

96 

245.4 

«?5-5 

57 

47-3 

3i-9 

17 

57-o 

65-4 

77 

146.  7 

99.0 

37 

196.5 

132-5 

97 

246.  2 

166.  i 

58 

48.  i 

32-4 

18 

97-2 

66.  o 

78 

147.6 

99-5 

38 

197-3 

'33-  ' 

90 

247.1 

166.6 

59 

48.9 

33-o 

J9 

98.7 

66.5 

79 

148.4 

IOC.  I 

39 

198.  i 

'33-6 

99 

247.9 

167.  2 

60 

49-  7 

33-6 

20 

99-5 

67.1 

80 

1*49-2 

loo.  7 

40 

199.0 

'34-2 

300 

248.7 

167.8 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

[For  56  Degrees. 

147 


DIFFERENCE  OF  LATITUDE 

DEPARTURE  FOR 

AND 

35°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Cist. 

Lat. 

Dep. 

I 

0.8 

0.6 

6l 

50.  o 

35-0 

121 

99-  I 

69.4 

181 

148.3 

103.  8 

241 

197-4 

138.2 

2 

1.6 

I.  I 

62 

50.  8 

35-6 

22 

99-9 

70.  o 

82 

149.  I 

104.4 

42 

198.2 

IjS.S 

3 

2-5 

'•7 

63 

5'.6 

36-1 

23 

100.  8 

70.5 

83 

149.9 

105.  o 

43 

199.  I 

139-4 

4 

3-3 

2-3 

64 

52.4 

36-7 

24 

101.  6 

71.1 

84 

I50-7 

105.5 

44 

199.9 

(40.  o 

5 

4.1 

2.9 

65 

53-2 

37-3 

25 

102.  4 

71.7 

85 

I5I-5 

1  06.  i 

45 

200.  7 

140.5 

6 

4-9 

3-4 

66 

54-  i 

37-9 

26 

103.  2 

72.3 

86 

152.4 

106.  7 

46 

201.  5 

141.  I 

7 

5-7 

4.0 

67 

54-9 

38-4 

27 

104.  o 

72.8 

87 

153-2 

I07-3 

47 

202.  3 

141.7 

8 

6.6 

4.6 

68 

55-7 

39-o 

28 

104.  9 

73-4 

88 

154.0 

107.8 

48 

203.  I 

142.2 

9 

7-4 

5-2 

69 

56.5 

39-6 

29 

105.7 

74.0 

89 

'54-8 

108.4 

49 

204.  o 

[42.8 

10 

8.2 

5-7 

70 

57-3 

40.  2 

3° 

1  06.  5 

74.6 

90 

'55-6 

109.  o 

5° 

204.  8 

143-4 

II 

9.0 

51 

7' 

58.2 

40.7 

'3' 

107-3 

75-' 

191 

'56-5 

109.  6 

251 

205.6 

144.0 

12 

9.8 

6.9 

72 

59.0 

4'-3 

32 

108.  i 

75-7 

92 

'57-3 

no.  i 

52 

206.  4 

144-5 

13 

10.  6 

7-5 

73 

59.8 

41.9 

33 

108.  9 

76-3 

93 

158.  i 

no.  7 

53 

207.  2 

145.1 

14 

11.5 

8.0 

74 

60.6 

42-4 

34 

109.  8 

76.9 

94 

158.91 

in.  3 

54 

208.  1 

145-7 

15 

12.  3 

8.6 

75 

61.4 

43-° 

35 

no.  6 

77-4 

95 

159-  7 

in.  8 

55 

208.  9 

146.  3 

16 

'3-i 

9-2 

76 

62.3 

43-6 

36 

111.4 

78.0 

96 

160.  6 

112.  4 

56 

209.  7 

146.8 

17 

13-9 

$.8 

77 

63.1 

44.2 

37 

112.  2 

78.6 

97 

It:  I.  4 

113.  o 

57 

210.  5 

147.4 

18 

14.7 

10.3 

78 

63-9 

44-  7 

38 

113.  o 

79-2 

98 

162.  2 

113.6 

58 

211.  3 

148.  o 

19 

15.6 

10.  9 

79 

64,7 

45-3 

39 

'13-9 

79-7 

99 

163.  o 

114.  1 

59 

212.  2 

148.6 

20 

16.  4 

11.5 

80 

65-5 

45-9 

40 

114.  7 

80.3 

200 

163.8 

114.7 

60 

213.  o 

149.1 

21 

17.2 

12.  0 

Si 

66.  4 

46.5 

141 

115.5 

80.9 

201 

164.6 

i»5-3 

261 

2I3.8 

149-7 

22 

18.  o 

12.6 

82 

67.  2 

47-o 

42 

116.  3 

81.4 

02 

l65-5 

"5-9 

62 

214.  6 

150-3 

23 

18.  8 

'3-2 

83 

es.  o 

47.6 

43 

117.1 

82.0 

°3 

166.3 

116.  4 

63 

215-4 

150.9 

24 

19.7 

13-8 

84 

68.8 

48.2 

44 

118.  o 

82.6 

04 

167.  i 

117.  o 

64 

216.  3 

15I-4 

25 

20.5 

H-3 

85 

69.6 

48.8 

45 

118.  8 

83.2 

°5 

167.9 

117.  6 

65 

217.  i 

152.  o 

26 

21-3 

14.9 

86 

70.4 

49-3 

46 

119.  6 

83-7 

06 

168.7 

118.2 

66 

217-9 

152.  6 

27 

22.  I 

'5-5 

87 

7'-3 

49-9 

47 

120.  4 

84-3 

°7 

169.  6 

118.  7 

67 

218.7 

153-1 

2» 

22-9 

16.  i 

88 

72.1 

5°-5 

48 

121.  2 

84.9 

08 

170.4 

119-3 

68 

219.5 

153-7 

29 

23.8 

16.  6 

89 

72.9 

51.0 

49 

122.  I 

85-5 

09 

171.  2 

119.9 

69 

220.  4 

154.3 

3° 

24.6 

17.2 

90 

73-7 

51.6 

5° 

122.  9 

86.0 

IO 

172.  o 

120.  5 

70 

221.  2 

154.9 

3i 

25.4 

17.8 

9' 

74-5 

52.2 

'5' 

123-7 

86.6 

211 

172.8 

121.  O 

271 

222.  O 

155-4 

S2 

26.2 

18.4 

92 

75-4 

52.8 

52 

124.5 

87.2 

12 

173-7 

121.  6 

72 

222.8 

156.0 

33 

27.0 

18.  9 

93 

76.2 

53-3 

53 

'25-3 

87.8 

13 

"74-5 

122.  2 

73 

223.  6 

156.6 

34 

27.9 

19.5 

94 

77.0 

53-9 

54 

126.  i 

88.3 

14 

•75-3 

122.7 

74 

224.4 

157.2 

35 

28.7 

20.  I 

95 

77.8 

54-5 

55 

127.  o 

88.9 

'5 

176.  i 

'23-3 

75 

225-3 

157-7 

36 

29.5 

20.  6 

96 

78.6 

55-i 

56 

127.8 

89.5 

16 

176.9 

123-9 

76 

226.  I 

i5«-3 

37 

3°-3 

21.  2 

97 

79-5 

55-6 

57 

128.6 

90.  i 

17 

177-8 

124-5 

77 

226.  9 

158.9 

38 

3'-1 

21.8 

98 

80.3 

56.2 

58 

129.4 

90.  6 

18 

178.6 

125.  o 

78 

227.  7 

159-5 

39 

3'-9 

22.4 

99 

81.1 

56.8 

59 

130.  2 

91.2 

19 

179-4 

125.6 

79 

228.5 

1  60.  o 

40 

32-8 

22.  9 

loo 

81.9 

57-4 

60 

I3I.I 

91.  8 

20 

180.2 

120.  2 

80 

229.4 

1  60.  6 

41 

33-6 

23-5 

101 

82.7 

57-9 

161 

I3I-9 

92-3 

221 

181.0 

126/8 

281 

230.  2 

161.  2 

42 

34-  4 

24-  I 

02 

83.6 

58-5 

62 

132.7 

92-9 

22 

181.9 

127-3 

82 

231.  o 

161.  7 

43 

35-2 

24.7 

03 

84-4 

59-  ' 

63 

133-5 

93-5 

23 

182.  7 

127.9 

83 

231.8 

162.  3 

44 

36.  o 

25.2 

04 

85.2 

59-7 

64 

'34-3 

94-  i 

24 

183-5 

128.  5 

84 

232.  6 

162.9 

45 

j6.  9 

25.8 

05 

86.0 

60.  2 

65 

•35-2 

94.6 

25 

184-3 

129.  i 

85 

233-5 

l63-5 

46 

37-7 

26.  4 

06 

86.8 

60.8 

66 

136.  o 

95-2 

26 

185.  i 

129.  6 

86 

234-3 

164.  o 

47 

38.5 

27.0 

07 

87.6 

61.  4 

67 

136.8 

95-8 

27 

185.9 

130.  2 

87 

235-  i 

164.6 

48 

39-3 

27-5 

08 

88.5 

61.  9 

68 

I37-6 

96.4 

28 

186.8 

130.8 

88 

235-9 

165.  2 

49 

40.  i 

28.  i 

09 

«9-3 

62.5 

69 

138.4 

96.9 

29 

187.  6 

'3'-3 

89 

236.  7 

165.8 

50 

41.  o 

28.7 

10 

90.  i 

63., 

70 

'39-3 

97-5 

3° 

188.4 

i3i-9 

90 

237.6 

I66.J 

5' 

41.8 

29-3 

in 

90.9 

63-7 

'71 

140.  i 

98.  i 

23' 

189.2 

132-5 

291 

238.4 

1  66.  9 

52 

42.  6 

29.8 

12 

9'-7 

64.2 

72 

140.9 

98.7 

32 

190.  o 

I33-' 

92 

239.2 

167.5 

53 

43-4 

3°-4 

'3 

92.  6 

64.8 

73 

141.  7 

99.2 

33 

190.9 

133-  6 

93 

240.  o 

1  68.  i 

54 

44.2 

31.0 

14 

93-4 

65.4 

74 

142.5 

99-8 

34 

191.7 

134.2 

94 

240.  8 

168.6 

55 

45-  « 

3'-5 

15 

94.2 

66.0 

75 

143.4 

100.  4 

35 

192.5 

134.  8 

95 

241.6 

169.  2 

56 

45-9 

32.1 

16 

95.0 

66.5 

76 

144.2 

TOO.  9 

56 

"93-3 

135-4 

96 

242.5 

169.8 

57 

46.7 

32-7 

17 

95.8 

67.1 

77 

145.0 

101.  5 

37 

194.  i 

135-9 

97 

243-3 

170.4 

5» 

47-5 

33-3 

i* 

96.  7 

67.7 

7» 

145.8 

102.  I 

38 

195.0 

i36-5 

98 

244-1 

170.9 

59 

48-3 

33-8 

'9 

97-5 

68.3 

79 

146.  6 

102.  7 

39 

195.8 

i37-i 

99 

244-9 

171.5 

60 

49.  I 

34-4 

20 

98.3 

68.  8 

80 

147.4 

103.  2 

40 

196.  6 

137-7 

300 

245-7 

172.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[For  55  Degrees. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  36°. 

Dirt. 

Lat. 

Dcp. 

Dlst.        Lat. 

Dcp. 

Dlst 

Lat. 

Dep. 

Di-t 

Lat. 

Dcp. 

Dlst. 

Lat 

Dcp. 

I 

0.8 

0.6 

Cl 

49-  4 

35-9 

121 

97-9 

71.  I 

iSi 

146.  4 

1  06.  4 

241 

195.0 

141.  7 

2 

1.6 

I.  2 

62 

50.2 

36.4 

22 

98.7 

71-7 

82 

147.2 

107.  o 

42 

195.8 

142.  2 

3 

2-4 

1.8 

63 

51.0 

37-0 

23 

99-  5 

72.3 

83 

I4S.  I 

107.  6 

43 

196.  6 

142.  S 

4 

3-2 

2-4 

64 

51.8 

37-6 

24 

loo.  3 

72.  9 

84 

148.9 

1  08.  2 

44 

197.4 

'43-  4 

s 

4.0 

2.9 

65 

52.6 

38-2 

25 

101.   I 

73-5 

85 

149.  7 

1  08.  7 

45 

198.  2 

144.0 

6 

4-9 

'  3-5 

66 

53-4 

38.8 

26 

101.  9 

74-  i 

86 

150.5 

109.3 

46 

199.  o 

144.6 

7 

5-  7 

4-1 

67 

54-2 

39-4 

27 

102.  7 

74-6 

87 

I5I-3 

109.9 

47 

199.8 

145.2 

S 

6.5 

4-7 

68 

55.0 

40.  o 

28 

103.  6 

75.2 

88 

152.  i 

no.  5 

48 

200.  6 

145-8 

9 

7-3 

5-3 

69 

55.8 

40.  6 

29 

104.4 

75-8 

89 

152.9 

in.  i 

49 

201.  4 

146.  4 

10 

8.  i 

5-9 

7° 

56.6 

41.  i 

3° 

105.  2 

76.4 

90 

'53-7 

in.  7 

5° 

202.  3 

146.  9 

II 

8.9 

6.5 

7' 

57-4 

41.7 

'31 

1  06.  O 

77.0 

191 

'54-5 

112.3 

251 

203.  I 

147-5 

12 

9-7 

7-  i 

72 

58.2 

42-3 

32 

106.8 

77-6 

92 

'55-3 

112.  9 

52 

203.9 

148.  I 

13 

10.5 

7.6 

73 

59-  « 

42.9 

33 

107.  6 

78.2 

93 

156.  i 

"3-4 

53 

204.  7 

148.7 

»4 

"•3 

8.2 

74 

59-9 

43-5 

34 

1  08.  4 

78.8 

94 

156.9 

114.  o 

54 

205.5 

149.3 

15 

12.  I 

8.8 

75 

60.  7 

44-  ' 

35 

109.  2 

79-4 

95 

157.8 

114.  6 

55 

206.  3 

149-9 

1  6 

12-9 

9-4 

/6 

61.5 

44-  7 

36 

no.  o 

79-9 

96 

158.  6 

115.2 

56 

207.  i 

150.5 

17 

I3.8 

10.  o 

77 

62.3 

45-3 

37 

no.  8 

80.  5 

97 

159.4 

115.8 

57 

207.9 

151.1 

18 

14.  6 

10.  6 

78 

63.1 

45.8 

38 

in.  6 

81.  i 

98 

160.  2 

no.  4 

58 

208.  7 

151.  6 

19 

"5-4 

II.  2 

79 

63-9 

46.  4 

39 

112.5 

81.7 

99 

161.  o 

117.0 

59 

209.5 

152.2 

20 

1  6.  2 

n.  8 

80 

64.  7 

^47.0 

40 

"3-3 

82-3 

200 

161.8 

117.  6 

60 

210.3 

152.8 

:i 

17.  o 

I2-  3 

81 

65-5 

47.6 

141 

114.  i 

82.9 

201 

162.6 

nil  i 

261 

211.  2 

153-4 

22 

17.8 

12.9 

82 

66.3 

48.  2 

42 

114.9 

83-5 

02 

163.4 

118.  7 

62 

212.  O 

154.0 

23 

18.6 

>3-5 

83 

67.1 

48.8 

43 

115.7 

84.  i 

03 

164.  2 

"9-3 

63 

212.8 

154.6 

24 

19.4 

14.  i 

84 

68.0 

49.  4 

44 

116.  5 

84.6 

04 

165.  o 

119.9 

64 

213.  6 

155.2 

20.  2 

14.  7 

8S 

68.8 

50.  o 

45 

"7-3 

85.2 

05 

165.8 

120.  5 

65 

214-4 

155.8 

26 

21.  O 

'5-3 

86 

69.6 

5°-  5 

46 

US.  I 

85.8 

06 

1  66.  7 

121.  I 

66 

215.2 

156.4 

27 

21.8 

15.9 

87 

70.4 

51.  i 

47 

118.  9 

86.4 

07 

167.  5 

121.  7 

67 

216.  o 

156.9 

28 

22.7 

16.5 

88 

71.2 

5«-  7 

48 

119.  7 

87.0 

08 

168.  3 

122.  3 

68 

216.8 

157-5 

29 

23-5 

17.0 

89 

72.0 

52-3 

49 

120.  5 

87.6 

09 

169.  i 

122.8 

69 

217.  6 

158.  I 

3° 

24-3 

17.6 

90 

72.8 

52.9 

5° 

121.4 

88.2 

10 

169.9 

•23-4 

70 

218.  4 

158.7 

3' 

25.  I 

1  8.  2 

9i 

73-6 

53-5 

'5' 

122.  2 

88.8 

211 

170.  7 

124.  o 

271 

219.  2 

159-3 

32 

25.9 

18.  8 

92 

74-4 

54-  i 

52 

123.  o 

89-3 

12 

171-5 

124.  6 

72 

220.  I 

159-9 

33 

26.7 

19.4 

93 

75-2 

54-7 

53 

123.8 

89.9 

'3 

172.3 

125.2 

73 

220.  9 

1  60.  5 

34 

27-5 

20.  O 

94 

76.  o 

55-3 

54 

124.  6 

90.5 

'4 

173-  i 

125.  8 

74 

221.  7 

161.  i 

35 

28-3 

20.  6 

95 

76.9 

55-» 

55 

125.4 

91.1 

15 

'73-9 

126.  4 

75 

222.  5 

161.6 

36 

29.  i 

21.  2 

96 

77-7 

56.4 

56 

120.  2 

91.7 

16 

174-  7 

127.  o 

76 

223.3 

162.  2 

37 

29.9 

21-7 

97 

78.5 

57.0 

57 

127.  o 

92-3 

17 

175-6 

127.5 

77 

224.  I 

162.8 

38 

3°-  7 

22-3 

98 

57.6 

58 

127.8 

92.9 

IS 

176.  4 

128.  i 

78 

224.9 

163.4 

39 

31-6 

22.  9 

99 

80.  i 

56.2 

59 

128.6 

93-5 

19 

177.2 

128.  7 

79 

225.7 

164.  o 

40 

3-4 

23-5 

IOO 

80.  9 

58.8 

60 

129.4 

94-  ° 

2O 

178.0 

"29-3 

80 

226.  5 

164.6 

41 

33-2 

24.  I 

lot 

81.7 

59-  4 

161 

'3°-3 

94.6 

221 

178.8 

129.9 

281 

227-3 

165.  2 

42 

34-° 

24.7 

02 

82.5 

60.  o 

62 

131.1 

95-2 

22. 

179.6 

"3°-5 

-82 

228.  i 

165.8 

43 
44 

34-8 
35-6 

25-3 
25.9 

o» 

04 

83.3 
84.1 

60.5 
61.  i 

63 
64 

.131-9 
132-7 

95-8 
96.4 

23 

24 

180.  4 

iSi.  2 

131.1 
IS'-? 

»3 

84 

229.  o 
229.8 

166.3 

166.  9 

45 

36-4 

26.5 

05 

84.9 

61.7 

65 

133-5 

97.0 

25 

182.0 

'32-3 

85 

230.6 

167.3 

46 

37-2 

27.0 

06 

85.8 

62.3 

66 

"34-3 

97.6 

26 

182.  8 

132.8 

86 

23'-  4 

168.1 

47 

38.0 

27.6 

07 

86.6 

62.  9 

67 

135-  i 

98.2 

27 

183.6 

"33-4 

87 

232.2 

168.  7 

48 

38.8 

28.2 

08 

87.4 

63-5 

68 

'35-9 

98.7 

28 

184.5 

134.0 

88 

233-0 

169.3 

49 

39-6 

28.8 

09 

88.2 

64.  i 

69 

136'  7 

99-3 

29 

'85-3 

134.6 

89 

233-8 

169.9 

50 

40.  5 

29.4 

10 

89.0 

64.  7 

70 

137-5 

99-9 

3° 

1  86.  i 

'35-2 

90 

234.6 

170-5 

5' 

41-3 

30.  o 

III 

89.8 

65.2 

171 

138-3 

100.  5 

23' 

iii6.  9 

135-  3 

291 

235-4 

171.  o 

52 

42.  i 

30.6 

12 

90.  6 

65.8 

72 

'39-2 

IOI.  I 

32 

187.7 

136.4 

92 

236.  2 

171.  6 

53 

42-9 

31-2 

»3 

91.4 

66.4 

73 

140.  o 

101.  7 

33 

1  88.  5 

137-0 

93 

237-0 

172.  2 

54 

43'7 

3i-7 

14 

92.2 

67.  o 

74 

140.  8 

102.  3 

34 

'89-3 

'37-5 

94 

237-9 

172.8 

55 

44-5 

32-3 

15 

93.0 

67.6 

75 

141.6 

102.  9 

35 

190.  i 

138.1 

95 

238.7 

173-4 

5§ 

45'  3 

32-9 

10 

93-8 

68.2 

76 

142.4 

J°3-5 

36 

190.9 

i38-7 

96 

239-5 

174.0 

57 

46.  i 

33-5 

17 

94-7 

68.8 

77 

143-2 

104.  o 

37 

191.7 

'39-3 

97 

240-3 

174.6 

53 

46.9 

34-1 

18 

95-5 

69.4 

78 

144.0 

104.  6 

38 

192.5 

139-9 

98 

241.  I 

175.2 

59 

4Z'7 

34-7- 

19 

96-3 

69.9 

P 

144.8 

105.  2 

39 

193.4 

140.5 

99 

241.9 

175-  7 

60 

48.5 

35'3 

20 

97.1 

70.5 

So 

145.6 

105.  8 

40 

194.2 

141.  I 

300 

242.  7 

1/6-3 

Cist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dcp. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

[For  54  Degrees. 

149 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  37°. 

Dist 

Lat 

Dep. 

Dist 

Lat 

J>ep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

I 

0.8 

0.6 

6l 

48.7 

36.7 

121 

96.6 

72.8 

181 

144.6 

108.9 

241 

192.5 

145-0 

2 

1.6 

1.2 

62 

49-5 

37-3 

22 

97-4 

73-4 

82 

145.4 

109.5 

42 

193-3 

145.6 

3 

2.4 

1.8 

63 

5°-3 

37-9 

23 

98.2 

74-o 

83 

146.  2 

no.  i 

43 

194.  I 

146.2 

4 

3-2 

2.4 

64 

51.1 

38.5 

24 

99-0 

74-6 

84 

146.9 

1  10.  7 

44 

194.9 

146.8 

5 

4.0 

3-° 

65 

51-9 

39-1 

25 

99-8 

75-2 

85 

147-7 

111.3 

45 

195.-  7 

147-4 

6 

4.8 

3-6 

66 

52.7 

39-  7 

26 

100.  6 

75-8 

86 

148.5 

in.  9 

46 

196.5 

148.  o 

7 

5-6 

4-2 

67 

53-5 

40.3 

27 

101.4 

76-4 

87 

149-3 

112.5 

47 

197-3 

148.6 

8 

6.4 

4.8 

68 

54-3 

40.9 

28 

102.2 

77-o 

88 

150.  I 

113.1 

48 

198.1 

149-3 

9 

7-2 

5-4 

69 

55-i 

41-5 

29 

103.  o 

77-6 

89 

150-9 

113-7 

49 

198.9 

149-9 

10 

8.0 

6.0 

70 

55-9 

42.  i 

30 

103.8 

78.2 

90 

I5I.7 

II4-3 

50 

199-7 

150-5 

ii 

8.8 

6.6 

71 

56.7 

42.7 

131 

104.  6 

78.8 

191 

152.5 

114.9 

251 

200.  5 

151.1 

12 

9.6 

7-2 

72 

57-5 

43-3 

32 

105.4 

79-4 

92 

153-3 

"5-5 

52 

201.  3 

151-7 

13 

10.  4 

7-8 

73 

58-3 

43-9 

33 

1  06.  2 

80.0 

93 

I54.I 

1  16.  2 

53 

202.  1 

152.3 

»4 

11.2 

8.4 

74 

59-i 

44-5 

34 

107.  o 

80.6 

94 

154-9 

II6.8 

54 

2O2.  9 

152.9 

15 

12.  0 

9.0 

75 

59-9 

45-1 

35 

107.8 

81.2 

95 

155-7 

"7-4 

55 

203.7 

153-5 

16 

12.8 

9-6 

76 

60.  7 

45-7 

36 

108.6 

81.8 

96 

156.5 

118.  o 

56 

204.5 

154.1 

17 

13-6 

10.  2 

77 

61.5 

46.3 

37 

109.4 

82.4 

97 

157-3 

118.6 

57 

205.2 

154.7 

18 

14-4 

\o.  8 

78 

62.3 

46.9 

38 

I  10.  2 

83.1 

98 

158.  I 

119.  2 

58 

206.  o 

155-3 

19 

15.2 

11.4 

79 

63-1 

47-5 

39 

III.  O 

83-7 

99 

158.9 

II9.8 

59 

206.8 

155-9 

20 

16.  o 

12.  O 

80 

63.9 

48.  i 

40 

in.  8 

84-3 

200 

I59.7 

120.  4 

60 

207.6 

156-5 

21 

16.8 

12.6 

81 

64.7 

48.7 

141 

112.  6 

84-9 

20  1 

160.  5 

121.  O 

261 

208.  4 

157.  i 

22 

17.6 

1.3-2 

82 

65-5 

49-3 

42 

"3-4 

85-5 

02 

161.3 

121.  6 

62 

209.  2 

157-7 

23 

18.4 

13-8 

83 

66.3 

50.  o 

43 

114.  2 

86.1 

°3 

162.  i 

122.2 

63 

210.  O 

158-3 

24 

19.2 

14-4 

84 

67.1 

50.6 

44 

115.  o 

86.  7 

04 

162.9 

122.8 

64 

210.8 

158.9 

25 

20.  o 

15.0 

85 

67.9 

51.2 

45 

II5.8 

87-3 

05 

163-7 

123-4 

65 

211.  6 

159-5 

26 

20.8 

I5.6 

86 

68.7 

51-8 

46 

116.  6 

87.9 

06 

164.5 

124,0 

66 

212.  4 

160.  i 

27 

21.6 

16.2 

87 

69.  5 

52.4 

47 

117.4 

88.5 

07 

I65-3 

124.  6 

67 

213.2 

160.  7 

28 

22.4 

1  6.  9 

88 

7°-3 

53-o 

48 

118.2 

89.1 

08 

1  66.  i 

125.  2 

68 

214.0 

161.3 

29 

23.2 

17-5 

89 

71.1 

53-6 

49 

119.  o 

89.7 

09 

166.9 

125.8 

69 

214.8 

161.9 

30 

24.0 

18.  i 

9° 

71.9 

54-2 

50 

119.8 

90-3 

10 

167-7 

126.4 

70 

215.  6 

162.  5 

31 

24,8 

18.7 

91 

72.7 

54-8 

151 

120.  6 

90.9 

211 

168.5 

127.0 

271 

216.4 

163.  i 

32 

25.6 

19-3 

92 

73-5 

55-4 

52 

121.4 

91-5 

12 

169-3 

127.6 

72 

217.  2 

163-7 

33 

26.  4 

19.9 

93 

74-3 

56.0 

53 

122.2 

92.1 

13 

170.  i 

128.2 

73 

218.  o 

164-3 

34 

27.  2 

20.  5 

94 

75-i 

56.6 

54 

123.0 

92.7 

H 

170.9 

128.8 

74 

218.  8 

164.9 

35 

28.0 

21.  I 

95 

75-9 

57.2 

55 

123.8 

93-3 

15 

I71-7 

129.  4  ' 

75 

219.6 

165-5 

36 

28.8 

21.7 

96 

76.7 

57.  a 

56 

124.6 

93-9 

16 

172.5 

130.0 

220.  4 

1  66.  i 

37 

29-5 

22-3 

97 

77-5 

58-4 

57 

125.4 

94-5 

17 

173-3 

130.  6 

77 

221.  2 

166.7 

38 

30.3 

22-9 

98 

78-3 

59-0 

58 

126.2 

95-i 

18 

174.1 

131.2 

78 

222.0 

167-3 

39 

40 

3'-i 
31-9 

23-5 
24.  I 

99 

IOO 

79-1 
79-9 

59.6 
60.2 

59 
60 

I27.O 
127.8 

£1 

19 

20 

174-9 

175-7 

131.8 
132.4 

79 
80 

222.8 

223.  6 

167.9 
168.5 

4' 

32-7 

24-7 

IOI 

80.  7 

60.8 

161 

128.6 

96.9 

221 

176.5 

133-0 

281 

224.4 

169.  i 

42 

33-5 

25-3 

02 

81.5 

61.4 

62 

129.4 

97-5 

22 

177-3 

133-6 

82 

225.  2 

169.7 

43 

34-3 

25.9 

03 

82.3 

62.  o 

63 

130.2 

98.1 

23 

178.  i 

134.2 

83 

226.  o 

1/0.3 

44 

35-1 

26.5 

04 

83.1 

62.6 

64 

I3I.O 

98-7 

24 

178.9 

134.8 

84 

226.S 

170.9 

45 

35-9 

27.3 

°5 

83-9 

63.2 

65 

I3I.8 

99-3 

25 

1/9-7 

'35-4 

SS 

227.  6 

I7I-5 

46 

36-7 

27.7 

06 

84.7 

63.8 

66 

132.6 

99-9 

26 

iSp.  5 

136.0 

86 

228.  4 

172.1 

47 
48 

&3 

28.3 
28.9 

07 
08 

85.5 
86.3 

64.4 
65.0 

67 
68 

133-4 
134-2 

loo.  5 

IOI.  I 

27 
28 

181-3 
182.  i 

136.6 
•37-2 

87 
88 

229.  2 
230.0 

172-7 
173-3 

49 

39-' 

29-5 

09 

87.  i 

65.6 

69 

I35.0 

101.  7 

29 

182.9 

137-8 

89 

230.8 

173-9 

So 

39-9 

30.  I 

IO 

87.8 

66.  2 

70 

135-8 

102.  3 

.1° 

183-7 

138-4 

90 

231.6 

174-5 

5i 

40.  7 

3°-7 

III 

88.6 

66.  a 

171 

136.6 

102.9 

231 

184-5 

i39.o 

291 

232-4 

175.1 

52 

41-5 

31-3 

12 

89.4 

67.4 

72 

I37.4 

103-5 

32 

is5-3 

139.6 

92 

233-2 

175-7 

53 

42-3 

31-9 

13 

9O.  2 

68.0 

73 

138.2 

104.  i 

33 

1  86.  i 

140.  2 

93 

234.0 

176-3 

54 

43-1 

32-5 

14 

91.  o 

68.6 

74 

139.0 

104.7 

34 

186.9 

140.  8 

94 

234-8 

176.9 

55 

43-9 

33-i 

15 

91.8 

69.  2 

75 

139.8 

105-3 

35 

187.7 

141.4 

95 

235.  6 

177-5 

56 

44-  7 

33-7 

It 

92.  6 

69.8 

76 

140.  6 

105.9 

36 

188.5 

142.0 

96 

236.4 

178.  I 

57 

45-5 

34-3 

17 

93-4 

70.4 

77 

141.4 

106.  5 

37 

189-3 

142.6 

97 

237-2 

178.7 

58 

46-3 

34-9 

18 

94.2 

71.0 

78 

142/2 

107.  i 

38 

190.  i 

143-2 

98 

238.0 

179-3 

59 

47.1 

35-5 

19 

95-0 

71.  -6 

79 

143.  o 

107.  7 

39 

190.9 

143-8 

99 

238.8 

1/9-9 

60 

47-9 

36.1 

20 

95.8 

72.2 

80 

143.8 

108.3 

40 

191.  7 

144.4 

300 

239-6 

180.5 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

[For  53  Degrees. 

150 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  38°. 

Dlst. 

Lat. 

Dep. 

Dlst. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dcp. 

I 

0.8 

0.6 

61 

48.1 

37-6 

121 

95-3 

74-5 

181 

142.  6 

III.4 

241 

189.9 

148.4 

2 

1.6 

I.  2 

62 

48.9 

38-2 

22 

96.  i 

75-  1 

82 

143-4 

112.  I 

42 

190.  7 

149.0 

3 

2.4 

i.S 

63 

49.6 

38.8 

23 

96.9 

75-7 

83 

144.  2 

II2.7 

43 

191.5 

149.6 

4 

3-2 

2-5 

64 

50.4 

39-4 

24 

97-7 

76-3 

84 

145.0 

"3-3 

44 

192.  3 

150.  2 

5 

3-9 

3-i 

65 

51.2 

40.  o 

25 

98.5 

77.0 

85 

145-8 

"3-9 

45 

193-  i 

150.8 

6 

4-7 

3-7 

66 

52-0 

40.  6 

26 

99-3 

77.6 

86 

146.  6 

114.5 

46 

'93-9 

151.5 

7 

5-5 

4-3 

67 

S2.8 

41.2 

27 

100.  I 

76.2 

87 

147.4 

II5-I 

47 

194.6 

152.  1 

8 

6-3 

4-9 

68 

53-6 

41.9 

28 

100.  9 

78.8 

88 

148.  i 

115.7 

48 

195-4 

152.7 

9 

5-5 

69 

54-4 

42-5 

29 

101.  7 

79-4 

89 

148^9 

I  ID.  4 

49 

196.  2 

153-3 

10 

7-9 

6.2 

7° 

55-  2 

43-  i 

3° 

102.  4 

80.0 

9° 

149-  7 

117.  o 

5° 

197.0 

153-9 

ii 

8.7 

6.8 

71 

55-9 

43-7 

131 

103.  2 

80.  7 

191 

150.5 

117.  6 

251 

197.8 

154-5 

12 

9-5 

7-4 

72 

56.7 

44-3 

104.  o 

81.3 

92 

>5!-3 

118.2 

S2 

198.6 

155.1 

13 

10.  2 

8.0 

73 

57-5 

44-9 

33 

104.  8 

81.9 

93 

152.1 

118.  8 

53 

199.4 

155.8 

«4 

II.  0 

8.6 

74 

58-3 

45.6 

34 

105.  6 

82.5 

94 

152.9 

119.4 

54 

2OO.  2 

156.4 

15 

ii.  8 

9.2 

75 

59-1 

46.2 

35 

1  06.  4 

83.1 

95 

153-7 

120.  I 

55 

200.  9 

157.0 

16 

12.6 

9-9 

76 

59-9 

46.8 

36 

107.  2 

83-7 

96 

154-5 

120.  7 

201.  7- 

157.6 

17 

'3-4 

10.5 

77 

60.  7 

47-4 

37 

1  08.  o 

84-3 

97 

155.2 

121.3 

57 

£62.  5 

158.2 

18 

14.2 

n.  i 

61.5 

48.0 

38 

1  08.  7 

85.0 

<* 

156.  o 

121.9 

58 

2°3-  3 

158.8 

19 

11.7 

79 

62.3 

48.6 

39 

109.5 

85.6 

99 

156.8 

.122-5 

59 

204.  i 

159-5 

20 

15.  8 

12-3 

80 

63.  o 

49-3 

40 

110.  3 

86.2 

200 

157.6 

123.  I 

60 

204.9 

1  60.  1 

21 

16.5 

12.9 

81 

63.8 

49-9 

141 

ii  i.  i 

86.8 

201 

158.4 

'23-7 

261 

205.  7 

1  60.  7 

22 

17-3 

'3-5 

82 

64.6 

50.5 

42 

in.  9 

87-4 

02 

150.  2 

124.4 

62 

206.  5 

161.  3 

23 

1  8.  i 

14.2 

83 

65.4 

51.1 

43 

112.7 

SH.  o 

°3 

1  60.  O 

125.  o 

63 

207.  2 

161.  9 

24 

18.9 

14.8 

84 

66.2 

51-7 

44 

113-5 

8U.  7 

04 

1  60.  8 

125.  6 

64 

208.  o 

162.  5 

25 

19.7 

I5-4 

67.  o 

52-3 

45 

114-3 

89-3 

°5 

161.  5 

126.  2 

65 

208.  8 

163.2 

26 

20.  5 

1  6.  o 

86 

67.8 

52.9 

46 

115.  o 

89.9 

06 

162.  3 

126.8 

66 

209.  6 

163.8 

27 

21.3 

16.  6 

87 

68.6 

53-6 

47 

115.8 

90.5 

°7 

163-1 

127.4 

67 

210.  4 

164.4 

28 

22.  I 

17.2 

88 

69.  3 

54.2 

48 

116.6 

91.1 

08 

163.9 

128.  1 

68 

211.  2 

165.  o 

29 

22.  9 

17-9 

89 

70.1 

54-8 

49 

117.4 

09 

164.  7 

128.  7 

69 

212.  O 

i6<|.  6 

3° 

23.6 

,8.5 

90 

70.9 

55-4 

5° 

118.  2 

92-3 

10 

165-5 

129.3 

70 

212.  8 

i6b.  2 

3i 

24.4 

19.  i 

91 

71.7 

56.  o 

151 

119.  o 

93.0 

211 

166.  3 

129.9 

271 

213.  6 

166.  8 

32 

25.2 

19-7 

92 

72-5 

56.6 

52 

119.8 

0.3.  6 

12 

167.1 

I30-5 

72 

214-3 

167.5 

33 

26.  o 

20.  3 

93 

73-3 

57-3 

53 

120.  6 

94.  2 

13 

167.8 

131.1 

73 

2I5.I 

1  68.  I 

34 

26.8 

20.  9 

94 

74-1 

57-9 

54 

121.  4 

94-8 

14 

168.6 

131.8 

74 

215.9 

1  68.  7 

35 

27.6 

2'-5 

95 

74-9 

58.5 

55 

122.  I 

95-4 

15 

169.4 

132.4 

75 

216.  7 

169.3 

36 

28.4 

22.  2 

96 

75-6 

59.1 

56 

122.  9 

96.  o 

16 

1/0.  2 

133-° 

76 

217.5 

169.9 

37 

29.2 

22.8 

97 

76.4 

59-7 

57 

123-7 

96.7 

17 

171.  o 

!33-6 

77 

218.3 

170.5 

38 

29.9 

23-4 

98 

77.2 

60.  3 

58 

124.5 

97-3 

18 

I7I.8 

134.2 

78 

219.4 

171.  2 

39 

3°-7 

24.  o 

99 

78.0 

61.  o 

59 

125-3 

97-9 

19 

172.  6 

134.  8 

79 

210.  9 

171.8 

40 

3'-5 

24.6 

100 

78.8 

61.6 

60 

136.  I 

98-5 

20 

173-4 

"35-4 

80 

220.  6 

172-4 

4i 

32-3 

25.2 

101 

79.6 

62.2 

101 

126.  9 

99-  i 

221 

174.2 

136.  i 

281 

221.  4 

173-0 

42 

33-1 

25-9 

02 

80.4 

62.8 

62 

127.7 

99-7 

22 

174-9 

i36-7 

82 

222.  2 

I73-6 

43 

33-9 

26.5 

°3 

81.2 

63-4 

63 

128.4 

100.  4 

23 

175-7 

137-3 

83 

223.  o 

174.2 

44 

34-7 

27.1 

04 

82.  o 

6A.  0 

64 

129.  2 

101.  O 

24 

176.5 

I37--9 

84 

223.8 

174.8 

45 

35-5 

27.7 

°5 

82.7 

64.6 

65 

130.  o 

loi.  6 

25 

177-3 

138-5 

85 

224.  6 

'75-5 

46 

36.2 

28.3 

06 

83-5 

65-3 

66 

130.8 

102.  2 

26 

178.  i 

I39.I 

80 

225.4 

176.1 

47 

37-o 

28.9 

°7 

84-3 

65.9 

6Z 

131.  6 

102.  8 

27 

178-9 

139.  8 

87 

226.  2 

1/6-7 

48 

37-8 

29.  6 

08 

85.  I 

66.5 

68 

132-4 

103.4 

28 

179-7 

140.4 

88 

226.  9 

177-3 

49 

38.6 

30.  2 

09 

85-9 

67.1 

69 

133-2 

104.  o 

29 

1  80.  5 

141.  o 

89 

227.7 

177-9 

5° 

39-4 

30.  8 

10 

86.7 

67-7 

70 

134.0 

104.7 

3° 

181.  2 

141.  6 

90 

228.5 

178.5 

5' 

40.  2 

31-4 

in 

87.5 

68.3 

I?' 

134-7 

i°5-3 

23i 

182.0 

142.  2 

291 

229.3 

179.2 

52 

41.0 

32.0 

12 

88.3 

69.  o 

72 

135-5 

105.9 

32 

182.8 

142.  8 

92 

230.  I 

179.8 

53 

41.8 

32-6 

13 

89.0 

69.6 

73 

136.3 

1  06.  5 

33 

183.6 

143-4 

93 

230.9 

1  80.  4 

54 

42.  6 

33-2 

H 

89.8 

70.2 

74 

I3M 

107.  I 

34 

184.4 

144.  I 

94 

231-  7 

181.0 

55 

43-3 

33-9 

1C 

90.  6 

70.  8 

137-9 

107.7 

35 

l8c.  2 

144-7 

95 

232.  5 

181.6 

5° 

44-  i 

34-5 

10 

91.4 

71.4 

76 

i38-7 

1  08.  4 

1  86.  o 

145-3 

06 

233-3 

182.  a 

57 

44-9 

35-  i 

17 

92.2 

72.0 

77 

139-5 

109.  o 

37 

186.  8 

145-9 

97 

234.0 

182.  9 

58 

45-7 

35-7 

18 

93-o 

72.6 

78 

140.3 

109.  6 

187-5 

146.5 

08 

234.3 

183.5 

59 

46-5 

36-3 

19 

93-8 

73-3 

79 

141.  I 

I  10.  2 

39 

188.3 

147-1 

99 

235-  6 

184.  i 

60 

47-3 

36-9 

20 

94.6 

73'  9 

So 

141.  8 

110.  8^ 

4° 

189.  i 

147.8 

300 

336.  f. 

184.7 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dlst 

Dep. 

Lat 

[For  52  Degrees. 

151 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  39°. 

DUt 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep 

.Dist. 

Lat 

Dep 

I 

0.8 

0.6 

6l 

47-4 

38.4 

121 

94.0 

76.1 

181 

140.  7 

"3-9 

241 

137-3 

151.  7 

2 

1.6 

1-3 

62 

48.2 

39-  ° 

22 

94.8 

76.8 

82 

141.4 

114.5 

42 

IS3.  I 

152.3 

3 

2-3 

1-9 

63 

49-o 

39.6 

23 

95.6 

77-4 

83 

142.  2 

115.2 

43 

188.8 

152.9 

4 

3-' 

2-5 

64 

49-7 

40-3 

24 

96.4 

78.0 

I4 

143.0 

115.8 

44 

189.  6 

153-6 

5 

3-9 

3-J 

% 

5°-5 

40.9 

2j 

97:  i 

78.7 

85 

J43-8 

116.4 

45 

190.4 

IC4.  2 

6 

4-7 

3-8 

66 

5'-3 

41-5 

20 

97-$ 

79-3 

86 

'44-5 

117.1 

46 

191.2 

154.8 

7 

5-4 

4.4 

67 

52.1 

42.2 

27 

98.7 

79-9 

87 

'45-3 

117.7 

47 

192.  o 

155-4 

8 

6.2 

5.0 

68 

^2.8 

42.8 

28 

99-5 

So.  6 

o5 
DO 

146.  i 

nS.  3 

4S 

192.7 

156.  1 

9 

7.0 

5-7 

69 

53-6 

43-4 

29 

100.  3 

81.2 

89 

146.9 

118.9 

49 

193  5 

156.7 

10 

7.8 

6-3 

70 

54-4 

44.1 

3° 

IOI.  O 

81.8 

90 

H7-7 

119.6 

50 

194.  3 

157-  3. 

ii 

8.5 

6.9 

71 

55-2 

44-7 

'3' 

101.  8 

82.4 

191 

148.4 

120.  2 

251 

195-  i 

150.  o 

12 

9-3 

7.6 

72 

56.0 

45-3 

32 

102.  6 

S3-' 

92 

149.2 

120.8 

52 

.195.  8 

158.6 

13 

10.  I 

8.2 

73 

56-7 

45-9 

33 

103.4 

83.7 

93 

150.  o 

121.  5 

53 

196.  6 

159.2 

14 

10.  9 

8.8 

74 

57-5 

46.6 

34 

104.  i 

84-3 

94 

150.8 

122.  I 

54 

197.4 

159.8 

15 

11.7 

9-4 

75 

58-3 

4^-2 

35 

104.9 

85.0 

95 

15I-5 

122.7 

55 

198.2 

160.5 

10 

12.4 

IO.  I 

7^ 

59-' 

47.8 

36 

105.7 

85.6 

96 

'S2-3 

1=3-3 

56 

198.9 

161.  1 

»7 

13.2 

10.  7 

77 

59/8 

48.5 

37 

1  06.  5 

86.2 

97 

'53-1 

124.  o 

57 

199-7 

161.  7 

18 

14.  o 

II.  8 

78 

60.6 

49-1 

33 

107.2 

86.8 

9S 

153-9 

124.6 

58 

200.  5 

162.4 

J9 

14.8 

12.0 

79 

61.4 

49-7 

39 

1  08.  o 

87.5 

99 

154-7 

125.2 

59 

201.  3 

I  S3-  0 

20 

'5-5 

12.6 

80 

62.2 

50-3 

40 

icS.  8 

88.1 

200 

155-4 

125-9 

60 

202.  I 

163.6 

21 

16.3 

13-2 

81 

62.  9 

51.0 

141 

leg.  6 

88.7 

201 

156.  2 

126.5 

261 

202.  8 

i°4-3 

22 

17.1 

13-8 

82 

63.7 

51.6 

42 

110.4 

89.4 

02 

157.0 

127.  I 

62 

203.  6 

1^4-9 

23 

i>9 

14-5 

83 

64-5 

52.2 

43 

in.  i 

90.  o 

<>3 

I57.8 

I27.8 

63 

204.4, 

165.5 

24 

18.7 

15.1 

84 

65-3 

52.9 

44 

in.  9 

90.  6 

04 

158-5 

128.4 

64 

205.  2 

1  56.  i 

25 

19.4 

'5-7 

85 

66.1 

53  5 

45 

112.  7 

91-3 

"5 

159-3 

129.  o 

65 

205.  9 

165.8 

26 

20.  2 

1  6.  4 

86 

65.8 

54-' 

46 

113.5 

91.9 

06 

1  60.  I 

129.  6 

66 

206.  7 

167.4 

27 

21.0 

17.0 

87 

67.6 

54-8 

47 

114.  2 

92.5 

07 

160.9 

ij°-3 

67 

207.5 

163.0 

88 

21.8 

17-6 

88 

68.4 

55-4 

48 

115.  o 

93-  ' 

08 

I6I.6 

130.9 

68 

208.  3 

i  to.  7 

29 

22-5 

18-  3 

89 

69.  2 

56.0 

49 

II5.8 

93-8 

09 

162.4 

'31-5 

69 

209.  i 

169.  3 

3° 

23-3 

18.9 

90 

69.9 

56.6 

5° 

II6.6 

94-4 

10 

163.  2 

132.  2 

/o 

200.  8 

169.9 

31 

24-1 

19.5 

9' 

70.7 

57-3 

'51 

"7-3 

95.0 

211 

164.  o 

132.8 

271 

2IO.  0 

i/o-S 

32 

24-9 

20.  I 

92 

71-5 

57-9 

52 

118.  i 

95-7 

12 

164.  8« 

133-4 

72 

211.4 

171.2 

33 

25.6 

20:  8 

93 

72-3 

58-5 

53 

118.9 

96-3 

13 

165.5 

134-0 

73 

212.2 

171.8 

34 

26.4 

21.4 

94 

73-  ' 

59-2 

54 

119.7 

96.9 

H 

166.3 

134-7 

74 

212.  9 

172.4 

35 

27.2 

22.0 

95 

73-8 

59-8 

55 

1  20.  5 

97-5 

15 

167.  1 

135-3 

75 

213-7 

173-1 

36 

28.0 

22.7 

96 

74-6 

60.4 

56 

121.  2 

98.2 

16 

167.9 

>35-  9  ' 

76 

214.5 

1  73-  -7 

37 

.28.8 

23-3 

97 

75-4 

61.0 

57 

122.0 

98.8 

17 

168.6 

136.6 

77 

215-3 

174-3 

38 

29.5 

23-9 

98 

76.2 

61.7 

5» 

122.8 

0-4 

18 

169.4 

137-2 

7? 

216.  o 

175.0 

39 

3°-3 

24-5 

99 

76.9 

62.  3 

59 

123.  6 

IOO.  I 

'9 

I/O.  2 

137-8 

79 

216.8 

175.6 

40 

3'-' 

25.2 

100 

77-7 

62.9 

60 

124-3 

100.  7 

20  , 

171.  o 

'38.  5 

80 

217.6 

176.  2 

4' 

3i-9 

25.8 

101 

7«-5 

63.6 

101 

125.1 

101.  3 

221 

171.7 

I39-I 

281 

218.4 

176.  8 

42 

32-6 

26.4 

02 

64-2 

62 

125.9 

101.9 

22 

172.5 

'39-7 

82 

2lg.  2 

177.5 

43 

3-3-4 

27.1 

°3 

80.  o 

64.8 

63 

126.  7 

102.  6 

.23 

173-3 

140.3 

83 

219-9 

178.  1 

44 

34-2 

27.7 

04 

80.8 

65-4 

64 

127.5 

103.  2 

24 

I74.I 

141.  o 

84 

220.  7 

178.7 

45 

35-o 

28.3 

°5 

81.6 

66.  i 

65 

128.2 

103.8 

25 

174.9 

141,6 

85 

221.  5 

•1/9-4 

46 

35-7 

28.9 

06 

82.4 

66.  7 

66 

129.0 

104.5 

26 

175-6 

142.  2 

86 

222-3 

I  So.  o 

47 

36-5 

29.  6 

07 

83-2 

6>3 

67 

129.8 

105.  1 

27 

176.4 

I42-9 

87 

223.0 

1,80.6 

48 

37-3 

30.2 

oS 

83-9 

68.0 

68 

130.  6 

105.7 

28 

177.2 

143-5 

88 

223.8 

!S«.2 

49 

38.1 

30.8 

09 

84-7 

68.  6 

69 

I3I-3 

106.  4 

29 

178.0 

I44-I 

89 

224.  6 

181.9 

5° 

38-9 

3'-  5 

IO 

85-5 

69.  2 

70 

132.1 

107.  o 

3° 

178.7 

144-7 

90 

225.4 

182.5 

5' 

39-6 

32-  » 

III 

86.3 

69.9 

i/i 

132.9 

1O7.  t> 

231 

179-5 

145.4 

291 

226.  1 

183.  1 

52 

40.4 

32-7 

12 

87.0 

70.5 

72 

'3>7 

1  03.  2 

32 

180.3 

146.  o 

92 

226.  9 

183.8 

53 

41.2 

33-4 

'3 

87.8 

7I.I 

73 

134-4 

108.  9 

33 

IS!.  I 

146.6 

93 

227-7 

184.4 

54 

42.  o 

34-o 

'4 

88.6 

71-7 

74 

135-2 

109.5 

34 

181.9 

147-3 

94 

228.5 

185.0 

55 

42.7 

34-6 

»5 

89.4 

72.4 

75 

136.  o 

1  10.  I 

35 

182.6 

147-9 

95 

229.3 

185.6 

«6 

43-5 

35-2 

16 

90.  i 

73-  ° 

76 

136.8 

1  10.  8 

3& 

183.4 

148.5 

96 

230.0 

186.3 

57 

44-3 

35-9 

17 

90.9 

73-6 

77 

137.6 

111.4 

37 

184.2 

149.1 

97 

230.8 

186.9 

58 

45-  * 

36.S 

18 

91.  i 

74-3 

78 

138-3 

112.  0 

38 

185.0 

149.8 

98 

231.  6 

'fZ-s 

59 

45-9 

->7-i 

19 

92.5 

74-9 

P 

I39-I 

112.  6 

39 

185.7 

i50-4 

99 

232.4 

iSS.  2 

60 

46.6 

37-8 

20 

93-3 

75-5 

80 

J39-9 

"3-3 

40 

IS6.5 

151.  o 

300 

233-1 

L8S.  8 

Dlst. 

Dep. 

Lat. 

Dlst 

Dep. 

La£. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[For  51  Degrees. 

152 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  40°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

l>ep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.8 

0.6 

61 

46.  7 

39-2 

121 

92.7 

77.8 

181 

'3s-  7 

1  1  6.  3 

241 

184.  6 

"54-9 

2 

'•5 

'•3 

62 

47-5 

39-9 

22 

93-5 

78.4 

82 

'39-  4 

1  17.  0 

42 

185.4 

155-6 

3 

2-3 

1.0 

63 

48.3 

40.  5 

23 

94-2 

79-  i 

83 

140.  2 

1  17.  6 

43 

186.  I 

156.  2 

4 

3-  ' 

2.6 

64 

49-0 

41.  1 

24 

95.0 

79-  7 

84 

141.  o 

118.3 

44 

iS6.  9 

156.8 

5 

3-8 

3-  2 

65 

49-8 

41.8 

25 

95-8 

80.3 

85 

141.  7 

uS.  9 

45 

187.7 

157-5 

6 

4.6 

3-9 

66 

50.  6 

42.4 

26 

96.5 

.    Si.  o 

86 

142-5 

119.  6 

46 

188.4 

158.  I 

7 

5-4 

4-5 

67 

5>-3 

43-  ' 

27 

97-3 

81.6 

87 

'43-3 

120.  2 

47 

189.  2 

158.8 

8 

6.  i 

5-  > 

68 

52.  i 

43-  7 

28 

98.  i 

82.3 

88 

144.0 

120.  8 

48 

190.  o 

159.4 

9 

6.9 

5-8 

69 

52.9 

44-  4 

29 

98.8 

82.  9 

89 

144-  8 

121.5 

49 

190.7 

160.  i 

lu 

7-7 

6.4 

7o 

53-6 

45.0 

3° 

99.6 

83.6 

90 

M5-5 

122.  I 

5° 

191.5 

160.  7 

II 

8.4 

7-  i 

71 

54-4 

45.6 

'3' 

100.  4 

84.2 

191 

146.3 

122.8 

25' 

'92-3 

161.  3 

12 

9-2 

7-7 

72 

55-2 

46.  3 

32 

101.  I 

84.8 

92 

147.  i 

123.4 

52 

193.  o 

162.  o 

13 

IO.  O 

8.4 

73 

55-9 

46.9 

33 

101.  9 

85-5 

93 

147.8 

124.  I 

53 

193-8 

162.6 

10.7 

9.0 

74 

56.7 

47-6 

34 

102.  6 

86.  i 

94 

148.6 

124.  7 

54 

194.6 

163-3 

ii 

11.5 

9.6 
10.3 

75 
76 

57-5 
58.2 

48.2 
48.9 

35 
36 

103.4 

104.  2 

86.8 
87.4 

$ 

149.4 
150.  i 

125-3 
126.  o 

55 
56 

195-3 
196.  i 

'63-9 
164.  6 

'7 

13.0 

jo.  9 

77 

59.0 

49-  5 

37 

104.  9 

88.  i 

97 

150.9 

126.6 

57 

196.9 

165.  2 

18 

13.8 

ii.  6 

78 

59-8 

50.1 

38 

105.7 

88.7 

98 

151.7 

127.  3 

58 

197.6 

165.8 

»9 

14.  6 

12.  2 

79 

60.  5 

50.  8 

39 

1  06.  5 

89-3 

99 

152.4 

127-9 

59 

198.4 

166.5 

20 

'5-3 

12.9 

So 

61.3 

51-4 

40 

107.  2 

90.  o 

200 

'53-2 

128.  6 

60 

199.2 

167.  I 

21 

16.  i 

"3-5 

81 

62.  o 

52.1 

141 

1  08.  o 

90.  6 

201 

154.0 

129.  2 

261 

199.9 

167.8 

22 

16.  9 

14.  i 

82 

62.8 

52-7 

42 

108.  8 

9'-3 

O2 

154-7 

129.  8 

62 

200.  7 

168.4 

23 

17.6 

14-8 

83 

63.6 

53-4 

43 

109.  5 

91.9 

°3 

'55-5 

130-5 

63 

20J.  5 

169.  1 

24 

18.4 

15.4 

84 

64-  3 

54.0 

44 

no.  3 

92.  6 

04 

'5".  3 

131.  i 

64 

202.  2 

169.  7 

25 
26 

19.2 
19.9 

16.  i 
16.7 

85 
86 

65.1 
65.9 

54-6 

55-3 

45 

46 

in.  i 

in.  8 

93-2 
93-8 

s 

157.0 
157-8 

131.8 
132-4 

§ 

203.  o 

203.8 

I70-3 
171.  o 

27 

20.  7 

17-4 

87 

66.6 

55-9 

47 

112.  6 

94-5 

07 

158.6 

I33-I 

67 

204.  5 

171.  6 

28 

21.4 

18.  o 

88 

67.4 

56.6 

48 

"3-4 

95-  ' 

08 

159-3 

133-7 

68 

205.3 

172-3 

29 

22.  2 

18.  6 

89 

68.2 

57-2 

49 

114-  i 

95-8 

09 

160.  i 

134-3 

69 

206.  I 

172.9 

3° 

23.0 

"9-3 

90 

6S.  9 

57-9 

5° 

114.9 

96.4 

IO 

160.  9 

'35-  ° 

70 

206.8 

173-6 

3' 

23-7 

19.9 

9' 

69.  7 

58-5 

151 

115.7 

97-  i 

211 

161.  6 

135-6 

271 

207.  6 

174.2 

32 

24.5 

20.  6 

92 

70.5 

59-  i 

52 

1  1  6.  4 

97-7 

12 

162.  4 

'36-3 

72 

208.  4 

174-8 

33 

25-3 

21.  2 

93 

71.2 

59-8 

53 

117.  2 

98.3 

'3 

163.  2 

136.9 

73 

209.  i 

'75-  S 

34 

26.  o 

21-9 

94 

72.0 

60.  4 

54 

118.  o 

99.0 

14 

163.9 

'37-6 

74 

209.9 

176.1 

26.8 

22.5 

95 

72.8 

61.  i 

55 

118.  7 

99.6 

'5 

164.  7 

138.  2 

75 

210.  7 

176.8 

36 

27.6 

23-  ' 

96 

73-5 

.61.7 

56 

119.5 

100.  3 

16 

'63-5 

138.8 

76 

211.  4 

177-4 

37 

28-3 

97 

74-3 

62.4 

57 

120.3 

joo.  9 

»7 

1  66.  2 

139-5 

77 

212.  2 

178.  i 

29.I 

24-4 

75-  ' 

63.  o 

58 

121.  O 

101.  6 

18 

167.  o 

140.  I 

7$ 

213.0 

178.7 

39 

29.9 

25.  I 

99 

75-8 

63.6 

59 

121.  8 

102.  2 

'9 

167.8 

140.  8 

79 

213-7 

179-3 

40 

30.  6 

25.7 

IOO 

76.6 

64-  3 

60 

J22.  6 

102.8 

20 

168.5 

141.  4 

80 

214.  5 

i  So.  o 

4' 

3!-4 

26.  4 

101 

77-4 

64.9 

161 

'23-3 

103.5 

221 

169.3 

142.  i 

281 

215-3 

180.6 

42 

32.2 

27.  o 

02 

78.1 

65.6 

62 

124.  I 

104.  I 

22 

170.  i 

142-  7. 

82 

216.  o 

181.  3 

43 

32-9 

27.  6 

03 

78.9 

66.2 

63 

124.9 

104.  8 

23 

170.8 

143-3 

83 

216.8 

181.9 

44 

33-7 

28.3 

04 

79-  7 

66.8 

64 

125.  6 

105.4 

24 

171.  6 

144.  o 

84' 

217.  6 

182.6 

45 

34-5 

28.  9 

°5 

80.4 

67.5 

65 

126.  4 

1  06.  i 

25 

172.4 

144.6 

85 

218.3 

183.  2 

46 

35-2 

29.  5 

06 

81.2 

68.  i 

66 

127.  2 

1  06.  7 

26 

I73-I 

145-3 

86 

219.  i 

183.8 

47 

36.0 

30.2 

°7 

82.0 

68.  8 

67 

127.9 

'07.3 

27 

173-  9 

145-9 

87 

219.9 

184-5 

48 

36.8 

3°-  9 

08 

82.7 

69.4 

68 

128.  7 

108.  o 

28 

174-7 

146.  6 

88 

220.  6 

185.  i 

49 

37-5 

3'-  5 

09 

83.5 

70.  I 

69 

129-5 

1  08.  6 

29 

1  75-  4 

147.2 

89 

221.4 

185.8 

50 

38.3 

32.1 

IO 

84-3 

70.7 

7° 

130.  2 

109.3 

3° 

1/6.  2 

147.8 

90 

222.  2 

186.4 

5' 

39-  ' 

32.8 

III 

85.0 

71-3 

171 

I3I.O 

109.9 

231 

177.0 

148.5 

291 

222.  9 

187.  i 

52 

39-8 

33-4 

12 

85.8 

72.0 

72 

I3I.8 

no.  6 

32 

'77-7 

M9-  ' 

92 

223.7 

187.7 

53 

40.  6 

34-  i 

"3 

86.6 

72.6 

73 

'32-  5 

III.  2 

33 

178.5 

149-  8 

93 

224.5 

188.3 

54 

41.4 

34-7 

87-3 

73-3 

74 

'33-3 

in.  8 

34 

1/9-3 

150.4 

94 

225.  2 

189.  o 

55 

42.  I 

35-4 

IS 

88.  i 

73-9 

75 

i34-i 

112.5 

35 

180.0 

151.1 

95 

226.  o 

189.6 

56 

42.  9 

36.  o 

88.9 

74-6 

75 

134.8 

113.1 

36 

180.  8 

15'-  7 

96 

226.  7 

190.3 

57 

43-7 

36.6 

17 

89.6 

75-2 

77 

'35-  6 

113.8 

37 

181.6 

'5--  3 

97 

227.5 

190.9 

5« 

44-4 

37-3 

18 

90.4 

75-8 

78 

136.4 

114.4 

38 

182.3 

98 

228.  3 

191.  6 

59 

45.2 

37-9 

'9 

91.2 

76.5 

79 

137.  i 

115.1 

39 

183.  i 

i  S3-6 

99 

229.  o 

192.  2 

60 

46.  o 

38-6 

20 

91.9 

77-i 

So 

'37-9 

115.7 

40 

183.9 

'54-3 

300 

229.  8 

192.8 

Dist 

Dep. 

I  -at. 

DUt. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

[For  50  Degrees. 

153 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  41°. 

Dlst. 

Lat. 

Dep. 

Dlst 

Lat 

Dep. 

Dlst 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dlst. 

Lat 

Dep. 

I 

0.8 

0.7 

61 

46.  0 

40.  o 

121 

91-3 

79-4 

181 

136.6 

118.7 

241 

181.9 

158.  I 

2 

'•  5 

62 

46.8 

40.7 

22 

92.1 

80.0 

82 

137-4 

119.4 

42 

182.6 

158.8 

3 

2-3 

2.0 

63 

47-5 

41-3 

23 

92.8 

80.  7 

83 

I38.I 

120.  I 

43 

183.  4 

>59-4 

4 

3-° 

2.6 

64 

48.3 

42.0 

24 

93-6 

81.4 

84 

138.9 

120.  7 

44 

184.  i 

1  60.  I 

5 

3-8 

3-3 

65 

49.1 

42.6 

25 

94-3 

82.0 

85 

139.6 

I2I.4 

45 

184.9 

1  60.  7 

6 

4-5 

3-9 

66 

49-8 

43-3 

26 

95-  ' 

82.7 

86 

140.4 

122.0 

46 

185.7 

161.4 

7 

5-3 

4.6 

67 

50.  6 

44.0 

27 

95.8 

83-3 

87 

141.  I 

122.7 

47 

186.4 

162.0 

g 

6.0 

5-2 

68 

5'-3 

44.6 

28 

96.  6 

84.0 

88 

141.9 

123-3 

48 

187.2 

162.  7 

9 

6.8 

5-9 

69 

52.1 

45-3 

29 

97-4 

84.6 

89 

142.  6 

124.  o 

49 

187.9 

163.4 

10 

7-5 

6.6 

70 

52.8 

45-9 

3° 

98.1 

85.3 

90 

143.  4 

124.7 

50 

188.7 

164.0 

it 

l>-3 

7.2 

71 

53-6 

46.  6 

131 

98.9 

85-9 

191 

144.1 

125-3 

251 

189.4 

164.7 

12 

9-« 

7-9 

72 

54-3 

47-2 

3? 

99.6 

86.6 

92 

144.9 

126.  o 

S2 

190.  2 

165-3 

13 

9-8 

8-5 

73 

55-1 

47-9 

33 

100.4 

87-3 

93 

'45-7 

126.6 

53 

190.9 

166.0 

'4 

10.  6 

9.2 

74 

55-8 

48-5 

34 

101.  I 

87.9 

94 

146.4 

127.3 

54 

I9I.7 

166.6 

IS 

"•3 

9.8 

75 

56.6 

49.2 

35 

101.9 

88.6 

95 

147.2 

127.9 

55 

192.5 

167-3 

16 

12.  I 

10.5 

57-4 

49-9 

36 

102.  6 

89.  -2 

96 

147.9 

128.6 

56 

193-2 

168.0 

17 

12.8 

II.  2 

77 

58.1 

50.5 

37 

103.4 

89-9 

97 

148.7 

129.2 

57 

194.0 

168.6 

18 

13.6 

n.8 

78 

53-9 

51.2 

38 

104.  1 

90.5 

98 

149.4 

129.9 

58 

194.7 

169.3 

19 

14-3 

12-5 

79 

59-6 

51.8 

39 

104.9 

91.2 

99 

150.2 

130.6 

'95-5 

169.9 

20 

15.1 

80 

DO.  4 

52.5 

40 

105.7 

91.8 

200 

150.9 

131.2 

60 

196.  2 

170.  6 

21 

15.8 

13-8 

bi 

61.  i 

53-  i 

141 

106.4 

92.5 

20  1 

151.7 

131.  9 

261 

197.0 

171.2 

22 

16.6 

14.4 

82 

61.9 

53-8 

42 

107.2 

93-2 

02 

152.5 

132-5 

62 

'97-7 

71.9 

23 

17-4 

15.1 

83 

62.6 

54-5 

43 

107.9 

93-8 

°3 

?53-2 

'33-2 

63 

198.5 

72.5 

24 

18.  i 

15-7 

84 

63-4 

55-' 

44 

1  08.  7 

94-5 

04 

154.0 

'33-8 

64 

199.2 

73-2 

3 

18.9 
19.6 

16.4 
17.1 

85 
8.5 

64.  2 
64.9 

55-8 
56.4 

a 

109.4 
no.  2 

95-'i 
95-8 

06 

'54-7 

'55-5 

'34'  5 
I35-I 

65 
66 

200.  o 

200.8 

73-9 
74-5 

27 

20.4 

17-7 

87 

65.7 

57-1 

47 

110.9 

96.4 

07 

156.2 

'35-8 

67 

201.  5 

75-2 

28 

2!.  I 

1  8.  .4 

88 

66.4 

57-7 

48 

111.7 

97.1 

08 

157.0 

136-5 

68 

202.  3 

75-8 

29 

21.  9 

19.  o 

89 

67.2 

53.4 

49 

112.  5 

97-8 

09 

I57.7 

I37-I 

69 

203.  o 

176.5 

3° 

22.6 

19.7 

90 

67-9 

59-o 

5° 

113.2 

98-4 

10 

158.5 

137-8 

70 

203.8 

177.  i 

31 

23-4 

20.  3 

9' 

68.7 

59-7 

151 

114.0 

99.1 

211 

159.2 

138.4 

271 

204.5 

177.8 

32 

24.2 

21.0 

92 

69.4 

60.4 

52 

114.7 

99-7 

12 

160.  o 

'39-1 

72 

205-3 

178.4 

33 

24.9 

21.6 

53 

70.2 

61.0 

53 

i'5-5 

100.4 

'3 

160.8 

139-7 

73 

206.  o 

179.1 

34 

25.7 

22.3 

94 

70.9 

61.7 

54 

no.  2 

IOI.  O 

'4 

161.  5 

140.4 

74 

206.8 

179-8 

35 

26.4 

23.0 

95 

71-7 

62.3 

55 

1  1  7.  O 

101.  7 

15 

162.  3 

141.  i 

75 

207.5 

180.4 

36 

27.2 

23.  6 

96 

72.5 

63.0 

56 

117.7 

102.  3 

1  6 

163.  o 

141.7 

7§ 

208.3 

181.  1- 

37 

27.9 

24-3 

97 

73-2 

63.6 

57 

u8.  5 

103.  o 

17 

163.6 

142.4 

77 

209.  1 

181.7 

38 

28.7 

24.9 

98 

74.0 

64-3 

S8 

119.  2 

103.7 

18 

164.5 

143.0 

78 

209.  8 

182.4 

39 

29.4 

25.6 

99 

74-7 

64.9 

59 

1  2O.  O 

104.3 

19 

165-3 

«43-7 

79 

2IO/6 

183.0 

40 

jj.  2 

26.  2 

100 

75-5 

65.6 

DO 

120.8 

105.0 

20 

166.  o 

'44-3 

80 

2ir.  3 

183-7 

41 

3°-9 

26.9 

101 

76.  2 

66.3 

161 

121.  5 

105.0 

221 

1  66.  8 

145.0 

281 

212.  I 

184.4 

42 

3'-7 

27.6 

02 

77.0 

66.9 

62 

122.3 

106.3 

22 

167.5 

145.6 

82 

212.8 

185.0 

43 
44 

32.5 
33-2 

28.2 
28.9 

03 
04 

77-7 
78.5 

67.6 
68.2 

63 
64 

123.  o 

123.8 

106.9 
107.  6 

23 
24 

168.3 
169.  i 

146.3 
147.0 

83 
84 

213.6 
214-3 

185.7 
186.3 

4I 
46 

34-0 
34-7 

29-5 
30.2 

3 

79.2 
80.0 

68.9 
69.5 

65 
66 

124-5 
'25.3 

1  08.  2 

108.  9 

20 

169.8 
170.  6 

147.6 
148.3 

85 
86 

215.  I 
215.8 

187.0 
187.  6 

47 

35-5 

30.8 

07 

80.8 

70.2 

67 

126.  o 

109.  6 

27 

'7'-  3 

148.9 

87 

216.6 

188.3 

48 

36.2 

3'-5 

08 

81.5 

70.9 

68 

126.8 

no.  2 

28 

172.1 

149.6 

88 

217.4 

188.9 

49 

37-JQ 

32.1 

09 

82.3 

7'-5 

69 

127.5 

110.9 

29 

172.8 

150.2 

89 

218.  i 

189.6 

5° 

37-7 

32.8 

10 

83.0 

72.2 

70 

128.3 

111.5 

3° 

173-6 

150.9 

90 

218.9 

190.3 

5« 

38-5 

33/5 

III 

83.8 

72.8 

171 

129.  I 

112.  2 

231 

174.3 

151-5 

291 

219.  6 

190.9 

52 

39-2 

34-1 

12 

84-5 

73-5 

72 

129.8 

112.  8 

32 

175.1 

152.  2 

92 

220.4 

191.6 

53 

40.  o 

34-8 

'3 

85.3 

74-' 

73 

130.6 

"3-5 

33 

175.8 

152.9 

93 

221.  I 

192.  2 

54 

40.8 

35-4 

86.0 

74-8 

74 

131.3 

114.  2 

34 

176.6 

«53-5 

94 

221.9 

192.9 

55 

41-5 

36.1 

15 

86.8 

75-4 

75 

132.1 

114.8 

35 

1  77.  4 

154.2 

95 

222.  6 

>93-  5 

56 

42-3 

36.7 

10 

87.5 

76.1 

76 

132.  8 

115.5- 

36 

178.  i 

154.8 

96 

223.4 

194.2 

57 

43-  ° 

37-4 

'7 

88.3 

76.8 

77 

13"".  6 

116.  i 

37 

178.9 

155-5 

97 

224.1 

.194.8 

58 

43-8 

38.1 

18 

89.1 

77-4 

78 

'34-3 

116.8 

38 

179.6 

156.1 

98 

224-9 

195-5 

59 

44-5 

38.7 

'9 

89.8 

78.1 

79 

'35-' 

117.4 

39 

I  So,  4 

99 

225.7 

190.  2 

00 

45-3 

39-4 

20 

90.  6 

78.7 

80 

135-8 

118.  1 

40 

181.  i 

»57r5 

300 

226.4 

196.8 

Dlst 

Dep. 

Lat 

Dlst. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dfst. 

Dep. 

Lat. 

[For  49  Degrees. 

154 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  42°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Di=t. 

Lat. 

Dtp. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat' 

Dep. 

I 

0.7 

°-7 

6l 

45-3 

40.8 

121 

89.9 

81.0 

181 

'34-S 

121.  I 

241 

179.  I 

161.  3 

2 

'•5 

'•3 

62 

46.  I 

41.5 

22 

90.  7 

81.6 

82 

'35-3 

121.  8 

tS 

179.8 

161.  9 

3 

2.  2 

2.  0 

63 

46.8 

42.2 

23 

91.4 

82-3 

83 

136.0 

'22-  5 

43 

ibo.  6 

162.6 

4 

3-° 

2-  7 

64 

47.6 

42.8 

24 

92.1 

83.0 

84 

136-  7 

123.  I 

44 

181.3 

"63-3 

e 

3-7 

3-3 

65 

48-3 

43-5 

25 

92-9 

83.6 

85 

137-5 

123.8 

45 

182.  i 

163-9 

6 

4-5 

4-Q 

66 

49.0 

44-  2 

26 

93-  6 

84-3 

86 

138.  2 

124.  5 

46 

182.8 

164.  6 

7 

5-2 

4-7 

67 

49-8 

44-  s 

27 

94-4 

85.0 

87 

139.  o 

125.  i 

47 

183.6 

'65-3 

8 

5-9 

5-4 

68 

5°-5 

45-5 

28 

95-  i 

85.6 

88 

'39-  7 

125.8- 

48 

184.3 

165.9 

9 

6.7 

6.0 

69 

Si-3 

46.  2 

29 

95-9 

86.  3 

89 

140.  5 

126.  5 

49 

185.  o 

166.6 

10 

7-4 

6-7 

70 

52.0 

46.8 

3° 

96.6 

87.0 

9° 

I-JI.2 

127.1 

5° 

185.8 

"67-3 

ii 

8.2 

7-4 

71 

52.8 

47-5 

"31 

97-4 

87.7 

191 

141.9 

127.8 

251 

1  86.  5 

168.  o 

12 

8.9 

8.0 

72 

53-5 

48.  2 

32 

98.  i 

88.3 

92 

142.7 

128.  5 

52 

i«7-3 

168.6 

"3 

9-7 

8.7 

73 

54.2 

48.8 

33 

98.8 

89.0 

93 

143-4 

129.  i 

53 

188.0 

169.3 

'4 

10.  4 

9-4 

74 

55.0 

49-  5 

34 

99.6 

89*.  7 

94 

144.  2 

129.  S 

54 

iSS.  8 

170.  o 

'5 

II.  i 

10.  o 

75 

55-7 

50.2 

35 

loo.  3 

9°-3 

95 

144-9 

i3o-5 

55 

189-5 

170.  6 

16 

II.  0 

10.  7 

76 

56-5 

50.9 

36 

IOI.  I 

91.  o 

96 

'45-7 

131.  i 

56 

190.  2 

I7I-3 

>7 

12.6 

11.4 

77 

57.2 

5'-5 

37 

101.8 

91.7 

97 

146.4 

131.8 

57 

191.  o 

172.0 

18 

13-4 

12.  0 

7s 

58.0 

52.2 

3» 

102.  6 

92-3 

98 

147.  i 

132-5 

53 

191.  7 

172.  6 

19 

14-1 

12.7 

79 

58.7 

52.9 

39 

103-3 

93-° 

99 

'47-9 

'33-2 

59 

192.5 

'73-3 

20 

14.9 

13-4 

80 

59-5 

53-5 

40 

104.  o 

93-7 

200 

148.6 

1.13.  8 

60 

193.2 

174.0 

21 

15.  6 

14.  I 

81 

60.  2 

54-2 

141 

1  04.  8 

94-3 

201 

149.  4 

'34-  5 

261 

194.0 

174.6 

22 

16.3 

14.7 

82 

60.  9 

54-9 

42 

105.5 

95.0 

02 

150.  i 

135-2 

62 

194-  7 

'75-3 

23 

17.1 

15.4 

«3 

61.7 

55-5 

43 

1  06.  3 

95-7 

°3 

150.9 

'35-8 

63 

'95-4 

176.0 

24 

17.8 

16.  I 

84 

62.4 

54.2 

44 

107.  o 

96.4 

04 

151.  6 

'36-5 

64 

196.  2 

176.7 

25 

18.  6 

I6.7 

85 

63-2 

56.9 

45 

107.8 

97.0 

°5 

'52-3 

137-2 

65 

196.9 

"77-3 

26 

19-3 

17.4 

86 

63-9 

57-5 

46 

108.5 

97-7 

06 

153-  i 

137-8 

66 

197-7 

178.0 

27 

20.  i 

18.  i 

87 

64.  7 

58.2 

47 

log.  2 

98.4 

07 

153-8 

138-5 

67 

198.4 

178.7 

28 

20.8 

18.7 

88 

65.4 

58-9 

48 

IIO.  0 

99-o 

08 

154.  6 

139.2 

68 

199.2 

'79-3 

29 

21.6 

19.4 

89 

66.  i 

59.6 

49 

no.  7 

99-  7 

09 

155-3 

139.8 

69 

199.9 

i  So.  o 

3° 

22.3 

20.  I 

90 

66.9 

60.  2 

5° 

111.5 

100.  4 

10 

156.  i 

140.  5 

TO 

200.  6 

i  So.  7 

3' 

23.0 

20-7 

9' 

67.  6 

60.  9 

i5' 

112.  2 

IOI.  O 

211 

156.  8 

141.  2 

271 

201.  4 

.181.3 

32 

23-8 

21.4 

92 

68.4 

61.6 

52 

113.  o 

101.  7 

12 

J57-5 

I4I.9 

72 

202.  I 

182.0 

33 

24.5 

22.  I 

93 

69.  i 

62.  2 

53 

i'3-  7 

102.  4 

'3 

I58-3 

142.  5 

73 

202.  9 

182.  7 

34 

25-3 

22.8 

94 

69.9 

62.  9 

54 

114.4 

103.  o 

«4 

159.0 

143-2 

74 

203.  6 

183-3 

35 

26.  o 

23-4 

95 

70.  6 

63.6 

55 

115.  2 

103-  7 

15 

159-8 

143.9 

75 

204.4 

184.  o 

36 

26.8 

24.  I 

96 

7i-3 

64.2 

56 

II5.9 

104.4 

Id 

1  60.  5 

144.  5 

76 

205.  I 

184.7 

37 

27.5 

24.8 

97 

72-1 

64.9 

57 

116.  7 

105.  i 

17 

161.  3 

145-2 

77 

205.9 

185-3 

38 

2$.  2 

25-4 

98 

72.8 

65.6 

58 

117.4 

105.  7 

18 

162.  o 

145.9 

78 

206.  6 

1  86.  o 

39 

29.  o 

26.  I 

99 

73-6 

65.  2 

59 

118.  2 

1  06.  4 

J9 

162.  7 

146.5 

79 

207-3 

1  86.  7 

40 

29.  7 

26.8 

IOO 

74-3 

66.9 

60 

118.9 

107.  i 

20 

l63-  5 

147.2 

80 

208.  i 

187.4 

41 

3°-S 

27.4 

101 

75-  i 

67.6 

161 

119.  6 

107.  7 

221 

164.  2 

147-9 

281 

208.8 

188.  o 

42 

31.2 

2<J.  I 

02 

75-8 

68-3 

62 

120.  4 

1  08.  4 

22 

165.  o 

148.5 

82 

209.  6 

1  88.  7 

43 

32.0 

28.8 

03 

76.5 

68.9 

63 

121.  I 

109.  I 

23 

165.7 

149.2 

83 

210.  3 

189.4 

44 

32-7 

29.4 

04 

77-3 

69.6 

64 

121.  9 

109.  7 

24 

1  66.  5 

149.9 

84 

211.  I 

190.  o 

45 

33-4 

30.  ! 

°5 

78.0 

7°-3 

65 

122.  6 

no.  4 

25 

167.  2 

150.  6 

85 

211.  8 

190.  7 

46 

34-2 

30.  8 

06 

78.8 

70.9 

66 

123.4 

ill.  i 

26 

168.0 

151.  2 

86 

212.  5 

191.4 

47 

34-9 

3'-4 

07 

79-5 

71.6 

67 

124.  I 

111.7 

27 

1  68.  7 

151.9 

fr 

213-3 

192.  o 

48 

35-7 

32-1 

08 

So.  3 

72-3 

63 

124.  8 

112.  4 

28 

169.4 

152.  6 

88 

214.  o 

192.  7 

49 

36-4 

32-8 

•  09 

81.0 

72.9 

69 

125.  6 

113.1 

29 

170.  2 

153.2 

89 

214.8 

'93-4 

5° 

37-2 

33-5 

10 

81.7 

73-6 

7° 

126.  3 

113.8 

3° 

170.  9 

153-9 

90 

215.5 

194.0 

5' 

37-  ° 

34-1 

III 

pTj 

74-3 

I7« 

127.  i 

114.4 

23' 

171-7 

154.6 

291 

216.  3 

«94-  7 

52 

38.6 

34-8 

12 

83.  2 

74-9 

72 

127.  8 

115.1 

32 

172.4 

155.2 

92 

217.  o 

195.4 

53 

39-4 

35-5 

13 

84.0 

75-6 

73 

128.6 

115.8 

33 

'73-2 

'55-9 

93 

217.7 

196.  i 

54 

40.  i 

36.1 

14 

84.7 

7<5.3 

74 

229.3 

116.  4 

34 

173-9 

156.  6 

94 

218.5 

196.7 

SI 

40.9 

36.8 

'I 

o!'s 

77.0 

75 

130.  i 

117.1 

35 

174.6 

157.2 

95 

219.  2 

197-4 

56 

41.6 

37-5 

10 

86.2 

77.6 

76 

130.  8 

117.  8 

36 

175.4 

157.9 

96 

22O.  O 

198.  i 

57 

42.4 

3f'i 

'7 

86.9 

7§-3 

77 

I3I-5 

118.4 

37 

176.1 

158.6 

97 

220.  7 

198.7 

S8 

43-1 

38.8 

18 

ll--7 

79.0 

78 

>32-3 

119.  1 

38 

176.9 

'59-3 

98 

221.  5 

199-4 

59 

43-8 

39.5 

'9 

88.4 

79.  .6 

79 

'33-0 

119.8 

39 

177.6 

'59-9 

99 

222.  2 

200.  I 

60 

44.6 

40.  i 

20 

89.2 

80.3 

BO 

133-8 

izo.  4 

40 

178.4 

loo.  6 

300 

222.  9 

200.  7 

Dist. 

Dep. 

Lat. 

Dist. 

Dc?. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1    Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[For  48  Degrees. 

155 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  43°. 

Dist. 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dlst 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

I 

0.7 

o.  7 

61 

44-  6 

41.6 

121 

88.  5 

82.S 

181 

132.4 

123.4 

241 

176.3 

164.4 

2 

'•5 

1.4 

62 

45-3 

42.3 

22 

89.  2 

83.  2 

82 

I33.  I 

124.  I 

42 

177-0 

165.  o 

3 

2.  2 

2.  O 

63 

40.  i 

43-o 

23 

90.  o 

83-9 

83 

133-8 

124.8 

43 

177-  7 

165.  7 

4 

2-9 

2-  7 

64 

46.8 

43-  6 

24 

90.  7 

84.6 

84 

134.6 

125.5 

44 

178.5 

1  66.  4 

5 

3-7 

3-4 

65 

47-5 

44-3 

25 

91  4 

85.2 

85 

135-3 

126.  2 

45 

179.2 

167.  i 

6 

4-4 

4-  l 

66 

48-3 

45  o 

26 

92.  2 

85.9 

86 

136.  o 

126.  9 

46 

179-9 

167.8 

7 

5-1 

4.8 

6? 

49-  o 

45-7 

27 

92.9 

86.  6 

87 

136.8 

127-  5 

47 

1  80.  6 

168.5 

8 

5-9 

5-5 

68 

49-  7 

46.  4 

28 

93-  6 

87-3 

88 

137.5 

128.  2 

48 

181.4 

169.  i 

9 

6.6 

6.  i 

69 

50.5 

47-1 

29 

94-3 

88.0 

89 

138.2 

128.  9 

49 

182.  I 

169.8 

10 

7-3 

6.8 

70 

51-  2 

47-  7 

3° 

95-i 

88.  7 

90 

139.0 

129.  6 

5° 

182.8 

170.5 

ii 

8.0 

7-5 

71 

51.9 

48.  4 

131 

95.8 

89-  3 

191 

I39-  7 

130-3 

251 

183.6 

171.2 

12 

8.8 

8.2 

72 

52.7 

49-  I 

32 

96.5 

90.  o 

92 

140.4 

130.9 

S2 

184.3. 

171.9 

'3 

9-5 

8.9 

73 

53-4 

49-8 

33 

97-3 

90.  7 

93 

141.  2 

131.  6 

53 

185.  o 

172.5 

14 

10.  2 

9-5 

74 

54-1 

5°-5 

34 

98.0 

91.4 

94 

141.9 

132-3 

54 

185.8 

173-2 

15 

II.  0 

10.  2 

75 

54-9 

51   i 

35 

98.7 

92.  i 

95 

142.  6 

133-0 

55 

186.5 

173-9 

16 

ii.  7 

10.  9 

76 

55-6 

51   8 

36 

99-  5 

92.  8 

96 

143-3 

J33-7 

56 

187.2 

174.6 

17 

12.4 

ii.  6 

77 

56-3 

52-5 

37 

100.  2 

93-4 

97 

144.  i 

I3V4 

57 

188.  o 

175.  3 

18 

13.2 

I2-3 

78 

57-o 

53-2 

38 

loo.  9 

94-  i 

98 

144.8 

135-0 

58 

1  88.  7 

176.  o 

19 

13.9 

79 

57.8 

53-9 

39 

101.  7 

9V  8 

99 

145-5 

!35-  7 

59 

189.4 

176.6 

20 

14.6 

\ll 

80 

58-5 

54.6 

40 

1  02.  4 

95-5 

200 

146.3 

136.  4 

60 

190.  2 

177-3 

21 

15.4 

14-3 

81 

59-2 

55-2 

141 

103.  i 

96.  2 

201 

147  o 

137-  i 

261 

190.9 

1/8.  0 

22 

16.  i 

15.0 

82 

60.  o 

55-9 

42 

103.9 

96.8 

O2 

147-  7 

137.8 

62 

191.  6 

178.7 

23 

16.  8 

15-7 

83 

60.  7 

56.6 

43 

104.  6 

97-5 

03 

148.5 

138.4 

63 

192.3 

179-4 

24 

17.6 

1  6.  4 

84 

61.  4 

57-3 

44 

105-3 

98.2 

04 

149    2 

139-  i 

64 

193-  i 

1  80.  O 

25 

18-3 

17.0 

85 

62.  2 

5!  o 

45 

106.  o 

98.9 

05 

149.9 

139.8 

65 

193-8 

i  So.  7 

26 

19.  o 

17.7 

86 

62.  9 

58-7 

46 

1  06.  8 

99.6 

06 

150-  7 

140.  5 

66 

194-5 

181,4 

27 

19.  7 

18.4 

87 

63.  6 

50-3 

47 

107-5 

100.3 

07 

151-4 

141.  2 

67 

195-3 

182.-  1 

28 

20.5 

19.1 

88 

6+-  4 

60.  o 

48 

loS.  2 

loo.  9 

08 

152.  i 

I4I.9 

68 

196.  o 

182.8 

29 

21.  -2 

19.  8 

89 

65.1 

60.7 

49 

109.  o 

101.  6 

09 

152-9 

142.5 

69 

196.7 

183-5 

3° 

21-9 

20.  5 

90 

65.8 

61.4 

5° 

ic9.  7 

1  02.  3 

10 

!53-6 

143-  2 

70 

1.97-5 

184.  i 

3' 

22.  7 

21.  I 

9' 

66.  6 

62.  i 

15' 

no.  4 

103.0 

211 

!54-  3 

H3-9 

271 

198.2 

184.8 

32 

23-4 

21.8 

92 

67-3 

62.7 

52 

III.  2 

103-7 

12 

155.0 

144.  6 

72 

198.  9 

185.5 

33 

24.  I 

22-5 

93 

68.  o. 

63.  4 

53 

in.  9 

104-3 

13 

155.8 

145-3 

73 

199-7 

186.2 

34 

24-  9 

23-2 

94 

68.  7 

64.1 

54 

112.  6 

105.  o 

14 

156.5 

145-9 

74 

200.  4 

186.9 

35 

25.6 

23-9 

95 

69-5 

64.8 

55 

113.4 

105.  7 

15 

157.2 

146.  6 

75 

201.  I 

187.5 

36 

2S.3 

24.  6 

96 

70.2 

65.  5 

56 

114.  I 

1  06.  4 

16 

158.0 

147-3 

76 

201.  9 

188.2 

37 

27.  i 

25.2 

97 

70.9 

66.2 

57 

ii  .8 

107.  i 

17 

158-7 

148.  o 

77 

202.  6 

1  88.  9 

3» 

27.8 

25.9 

98 

71.7 

66.8 

58 

115.  6 

107.8 

18 

159-4 

148.7 

78 

203-3 

189.6 

39 

28.5 

26.6 

99 

72-4 

67.5 

59 

116.  3 

1  08.  4 

19 

1  60.  2 

149.4 

79 

204.  o 

190-3 

40 

29-3 

27-3 

IOO 

73-  i 

68.2 

60 

117.  o 

109.  i 

20 

1  60.  9 

150.  o 

80 

204.  8 

191.  o 

4' 

30.  o 

28.  o 

101 

73-9 

68.9 

161 

117.  7 

109.  8 

22! 

161.6 

150.7 

281 

205.5 

191.  6 

42 

3°-  7 

28.6 

02 

74.6 

69.6 

62 

118.  5 

no.  5 

22 

162.4 

151.4 

83 

2o6.  2 

192-3 

43 

3i-4 

29-3 

03 

75-3 

70.2 

63 

119.  2 

ni.  2 

23 

163.  i 

152.  1 

83 

207.  o 

193-0 

44 

32.2 

30.0 

04 

76.1 

70.9 

64 

119.9 

in.  8 

24 

163.8 

152.8 

84 

207.7 

193-7 

45 

32-9 

3°-  7 

05 

76.  8 

71.6 

65 

120.  7 

112.5 

25 

164.6 

153-4 

85 

208.4 

194-4 

40 

33-6 

31-4 

06 

77.  5 

72-3 

66 

121.  4 

113.2 

20 

165.  3 

154.  1 

86 

209.  2 

195-  ' 

47 

34-4 

32-  i 

07 

7s-  3 

73-o 

67 

122.  I 

"3-9 

27 

1  66.  o 

154.8 

87 

209.  9 

195-7 

48 

35-i 

32-7 

08 

79.0 

73-7 

68 

122.  9 

114.  6 

28 

1  66.  7 

155-5 

88 

210.  6 

196.4 

49 

35-8 

33-4 

09 

79-7 

74-3 

69 

123.  6 

II5-3 

29 

167.5 

156.2 

89 

211.4 

197.  i 

5° 

36.6 

34-  I 

10 

80.4 

75-0 

124-3 

115.9 

3° 

168.2 

156.9 

9° 

212.  I 

197.8 

51 

37-3 

34-8 

in 

81.2 

75-7 

171 

I25.I 

116.  6 

231 

1  68.  9 

157.5 

291 

212.8 

198.5 

52 

38.0 

35-5 

12 

81.9 

76.4 

72 

125.8 

"7-3 

32 

169.7 

158.  2 

92 

213.  6 

199.  i 

53 

38.8 

36.1 

13 

82.6 

7.7.1 

73 

126.5 

118.0 

33 

170.4 

158.9 

93 

214-3 

199.8 

54 

39-5 

36.  8 

H 

83-4 

77-7 

74 

127-3 

118.  7 

34 

171.1 

159.6 

94 

215.  o 

200.  5 

55 

40.  2 

37-5 

15 

84.  i 

78.4 

75 

128.  o 

"9-3 

35 

171.9 

160.  3 

95 

215.  7 

201.  2 

56 

41.  o 

38.2 

16 

84.8 

79-  i 

76 

128.  7 

1  2O.  O 

36 

172.  6 

161.  o 

96 

216.5 

201.  9 

57 

41.  7 

17 

85.6 

79-8 

77 

129.4 

1  20.  7 

37 

173-3 

161.6 

97 

217.  2 

202.  6 

58 

42.4 

39-6 

18 

86.3 

80.5 

78 

130.  2 

121.  4 

38 

174.  i 

162.  3 

98 

217.9 

203.  2 

59 

43-  i 

40.2 

'9 

87.0 

81.2 

79 

130.9 

122.  I 

39 

174.8 

163.  o 

99 

218.  7 

203.9 

60 

43-9 

40.9 

20 

87.8 

81.8 

So 

131  6 

122.  8 

40 

'75-5 

163-  7 

300 

219.4 

204.  6 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dlst. 

Dep 

Lat. 

[For  47  Degrees. 

156 


DIFFERENCE  OF  LATITUDE 

AND  DEPARTURE  FOR  44°. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dkt. 

Lat. 

Dep. 

DiU. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

o-  7 

o.  7 

61 

43-9 

4--  4 

121 

87.0 

84.1 

iGl 

130.  2 

25-7 

241 

'73-4 

167.4 

2 

1-4 

1.4 

62 

4  ',6 

43-  I 

22 

87.8 

84.7 

82 

130.9 

26.4 

42 

174.  i 

l6S.  I 

3 

2.  2 

2.  I 

63 

45-3 

43-8 

23 

83.  5 

85.4 

83 

131.  6 

27.1 

43 

174.8 

I6S.8 

4 

2-9 

2.8 

64 

46.  o 

44-  5 

24 

89.2 

86.  i 

84 

132.4 

27.8 

44 

"75-5 

169.5 

5 

3-6 

3-5 

65 

46.8 

45-2 

25 

89.9 

86.8 

S5 

133-  i 

28.5 

45 

76.2 

170.  2 

6 

4-3 

4.* 

66 

47-5 

45.8 

26 

90.  6 

87.5 

B6 

'33-8 

29.  2 

46 

77-o 

170.9 

7 

5-° 

4-9 

67 

48.2 

46.  5 

27 

91.4 

88.2 

87 

'34-5 

29.9 

47 

77-7 

171-6 

8 

5-8 

5-6 

68 

48.9 

47.2 

28 

92.1 

88.9 

88 

135-2 

130.  6 

48 

78.4 

172.3 

9 

6.5 

6-3 

69 

49-6 

47-9 

29 

92.8 

89.6 

89 

136.  o 

i3'-3 

49 

79-  l 

173-0 

10 

7-2 

6.9 

70 

50.4 

48.6 

3° 

93-5 

9°-3 

90 

'36-7 

132.  o 

5° 

79.8 

1/3-7 

ii 

7-9 

7.6 

7' 

51.1 

49-3 

'3' 

94.2 

91.  o 

191 

137.4 

132-7 

251 

180.  6 

174-4 

12 

8.6 

8-3 

72 

51.8 

50.  o 

32 

95.0 

91.  7 

92 

138.  i 

133-4 

52 

181.3 

175-  i 

>3 

9-4 

9.0 

73 

52-5 

50.7 

33 

95-7 

92.4 

93 

138.8 

134-  I 

53 

182.0 

«75  7 

14 

10.  I 

9-7 

74 

53-2 

51.4 

34 

96.4 

93-  i 

94 

139.6 

134-8 

54 

182.  7 

176.4 

IS 

10.8 

10.4 

75 

54-0 

52-' 

35 

97-  i 

93-8 

95 

140.3 

'35-5 

55 

•83.4 

177.  i 

16 

"•5 

n.  I 

76 

54-7 

52-8 

36 

97.8 

94-5 

96 

141.0 

13^-2 

56 

184.2 

177.8 

>7 

12.  2 

ii.  8 

77 

55-4 

53-5 

37 

98.5 

95-2 

97 

141.  7 

136.8 

57 

184.9 

178.5 

18 

12.  9 

'2-5 

78 

5^ 

54-2 

33 

99-3 

95-9 

98 

142.4 

137-5 

58 

'85.6 

179.2 

19 

'3-7 

'3-2 

79 

56.  8 

54-9 

39 

ICO.  O 

96.  6 

99 

143-  i 

133.  2 

59 

186.3 

'79-9 

-o 

14.4 

'3-9 

80 

57-5 

55-6 

4° 

loo.  7 

97-3 

200 

143-  9 

138.9 

60 

187,  o 

180.6 

21 

15.1 

14.  6 

81 

5«-3 

56-3 

I.}  I 

101.  4 

97-9 

201 

144.  6 

139.  6 

261 

187-7 

lui.  3 

22 

15.8 

15-3 

82 

59.0 

57-0 

42 

102.  I 

98.6 

O2 

'45-  3 

140.3 

62 

188.5 

182.  o 

23 

16.5 

16.  o 

83 

59-7 

57-7 

43 

102.  9 

99-3 

°3 

146.  o 

141.0 

63 

189.  2 

182.7 

24 

17-3 

16.7 

84 

60.  4 

58.4 

44 

103.  6 

IOO.  O 

04 

146.7 

ML? 

64 

189.9 

183.4 

25 

18.  o 

'7-4 

85 

61.1 

59.0 

45 

104.3 

loo.  7 

°5 

147-5 

142.4 

65 

190.6 

184.  i 

26 

18.7 

18.  i 

86 

61.  9 

59-  7 

46 

105.  o 

101.4 

ob 

148.2 

143-  ' 

65 

I9I.3 

184.8 

27 

19.4 

18.  8 

87 

62.6 

60.  4 

47 

105.7 

IO2.  I 

°7 

148.  9 

M3.8 

67 

192.  I 

'85.5 

28 

20.  I 

19-5 

88 

63-3 

61.  i 

48 

io5.  5 

102.8 

08 

149.6 

144-5 

es 

192.8 

186.2 

29 

20.  9 

20.  I 

89 

64.  o 

61.8 

49 

107.  2 

'°3-5 

09 

I5°.3 

145-2 

69 

193-5 

186.9 

3° 

21.6 

20.8 

90 

64.7 

62.5 

5° 

107.9 

104.2 

10 

151.1 

145-9 

7° 

194.2 

IS7.6 

3' 

22.3 

21.5 

91 

65-5 

63.2 

>5i 

108.  6 

104.9 

211 

151.8 

146.  6 

271 

194.9 

188.3 

32 

23.0 

22.  2 

92 

66.2 

63-9 

52 

109.  3 

105.  6 

12 

152.5 

J47-3 

72 

195-7 

iSS.  9 

33 

23.7 

22.  9 

93 

66.9 

64.6 

53 

110.  I 

ic6.  3 

'3 

153-2 

148.  o 

73 

196.4 

189.6 

34 

24.5 

23-6 

94 

67.6 

65.3 

54 

1  10.  8 

107.0 

14 

153-9 

148.7 

74 

197-1 

190.3 

35 

25.2 

24-3 

95 

68.3 

66.  o 

55 

111.5 

107.  7 

15 

154-  7 

149.4 

75 

197-8 

191.  o 

36 

25.9 

25.  o 

96 

69.  l 

66.  7 

56 

112.  2 

lc3.  4 

16 

I55.4 

150.  o 

76 

198.5 

191.7 

37 

26.6 

25-7 

97 

69.8 

67.4 

57 

112.  9 

leg.  i 

17 

156.  i 

150.7 

77 

'99-3 

192.4 

38 

27-3 

26.  4 

98 

70.5 

68.  i 

58 

"3-7 

109.8 

18 

156.8 

151.4 

78 

20O.  O 

193-  i 

39 

28.  I 

27.  I 

99 

71.  c 

68.8 

59 

114.4 

no.  5 

'9 

157.5 

152.1 

P 

200.  7 

193-8 

40 

28.8 

27.8 

IOO 

71.9 

69.5 

60 

115.1 

in.  i 

20 

1  5s-  3 

152.8 

80 

2ol.  4 

•94-  5 

41 

29.5 

28.5 

101 

72.7 

70.  2 

161 

115.8 

in.  8 

221 

-159.  o 

1530 

281 

£02.  1 

195.  2 

4- 

30.2 

29.  2 

02 

73-4 

70.9 

62 

1  1  6.  5 

112.5 

22 

I59.7 

154.2 

82 

2O2.  9 

'95-9 

43 

3°-9 

29.  9 

03 

74-  i 

71-5 

63 

H7.3 

113.2 

23 

160.4 

154.9 

83 

203.  6 

196.  6 

'4 

3«-7 

30.  6 

04 

74-8 

72.2 

64 

I  10.  O 

II3-9 

24 

161.  1 

155.6 

84 

2°4-  3,. 

197-3 

45 

32.4 

3'-  3 

°5 

75-5 

72.9 

65 

118.  7 

114.  6 

25 

161.  o 

156.3 

85 

205.  o 

158.  o 

46 

33-1 

32.0 

06 

76.3 

73.6 

6$ 

119.4 

II5-3- 

26 

162.6 

157.0 

86 

205.  7 

198.7 

47 

33-8 

32.6 

07 

77.0 

74-3 

67 

1:0.  i 

116.  o 

27 

i63-3 

«57-7 

87 

206.  5 

199.4 

48 

34-5 

33-3 

08 

77-7 

75.0 

68 

120.8 

116.  7 

28 

164.  o 

158.4 

8S 

207.2 

200.  I 

49 

35-2 

34-0 

09 

78.4 

75-7 

69 

121.  6 

-U  7.  4 

29 

164.7 

159.  i 

89 

207.9 

200.  8 

5° 

36.  o 

34-7 

10 

79.  i- 

76.4 

70 

122.3 

118.  i 

3° 

165.4 

159.8 

90 

208.6 

201.  5 

51 

3°-7 

35-4 

III 

79.8 

77-' 

171 

123.  o 

1  1.3.  8 

231 

166.  2 

1  60.  5 

291 

209.3 

202.  1 

52 

37-4 

36.' 

12 

80.6 

77-8 

72 

'23.7 

"9-5 

32 

1  66.  9 

161.  2 

92 

210.  0 

202.8 

53 

3».i 

36.8 

•3 

8'-  3 

78.5 

73 

124.4 

120.  2 

33 

167.6 

161.  9 

93 

210.8 

203.5 

54 

38.8 

37-5 

14 

82.0 

79-2 

74 

125.2 

120.  9 

34 

168.  3 

162.6 

94 

211.  5 

204,  2 

55- 

39-6 

38-2 

15 

82.7 

79-9 

75 

125.9 

121.  6 

35 

169.  o 

163.  2 

95 

212.  2 

204.9 

56 

40-3 

3S-9 

16 

83-4 

80.6 

76 

126,6 

122,3 

36 

169.  8 

•63.9 

95 

212.  9 

205.  6 

57 

41.  o 

39-6 

17 

84.  2 

81.3 

77 

".27-  3 

123.  o 

37 

170.5 

164.6 

97 

213.6 

206.  3 

58 

41.  7 

40-3 

18 

84.9 

82.0 

78 

128.0 

123.  6 

3s 

171.2 

165.3 

98 

214.4 

207.  o 

g 

42.4 
43-2 

41.  o 
41.7 

19 

20 

85.6 
86.3 

82.7" 
83.4 

g 

128.8 
129.5 

124.3 
125.0 

39 

40 

171.9 
172.  6 

1  06.  O 

1  66.  7 

99 
300 

2I5.I 
215.8 

207.7 
208.4 

Dist. 

Dep. 

Lat. 

DUt. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

[  For  46  L)cgrees. 

157 


DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  45°. 

Disk 

Lot. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

•Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

I 

0.7 

0.7 

61 

43-  i 

43-1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2 

1.4 

1.4 

62 

43-8 

43-8 

22 

80.3 

86.3 

82 

128.7 

128.  7 

42 

I7I.I 

171.1 

3 

2.  I 

2.  I 

€3 

44-5 

44-  S 

23 

87.0 

87.0 

!3 

129.4 

129.4 

43 

171.8 

171.8 

4 
5 

2.8 

3-5 

2.8 

3-5 

64 
65 

43-3 
46.0 

43-3 
46.0 

24 

25 

*7  7 
88.4 

87.7 
88.4 

84 
Is 

130.  I 
IJ0.8 

130.  i 
130.8 

44 

45 

172.5 
173-2 

172.5 
173-2 

6 

4.2 

4.2 

66 

46.7 

46.  7 

26 

89.1 

89.1 

86 

131.5 

131-5 

4° 

'73-9 

173-9 

7 

4-9 

4-9 

67 

47-4 

47-4 

27 

89.8 

89.8 

87 

IJ2.3 

132.2 

47 

'74-7 

"74-7 

8 

5-7 

5-7 

68 

48.1 

48.  I 

28 

90.5 

90.5 

88 

132.9 

132-9 

48 

J75-4 

«75-4 

9 

6.4 

6.4 

69 

48.8 

48.8 

29 

91.2 

91.2 

89 

I33-6 

133-6 

49 

176.1 

1/6.  i 

10 

7-1 

7-« 

70 

49-  5 

49-  S 

3° 

9i-9_, 

91.9 

90 

I34._4 

134.4 

S2 

176.8 

176.8 

u 

7-8 

7-8 

7' 

50.2 

50.2 

131 

92.  6 

92.6 

191 

»35-  i 

I35-I 

2S' 

177-5 

177-5 

12 

8-5 

8-5 

72 

5°-9 

5°-9 

32 

93-3 

93-3 

92 

135-8 

'35-8 

52 

178.2 

178.2 

13 

9.2 

9.2 

73 

51.6 

51.6 

33 

94.0 

94-0 

93 

I36.S 

'36-5 

S3 

178.9 

178.9 

M 

9-9 

9-9 

74 

52-3 

52-3 

34 

94.8 

94.8 

94 

137-2 

'37-2 

5.4 

179.6 

179.6 

>5 

16 

10.  6 
"•3 

10.  6 
"•3 

75 
76 

53-o 
S3-  7 

£3-° 
£3-7 

35 
36 

96.2 

96.2 

95 
96 

I37.9 
138.6 

'37-9 
138.6 

s$ 

56 

180.3 

181.0 

iSo.  3 
iSi.o 

J7 

12.0 

12.0 

77 

54-4 

54-4 

37 

96.9 

96.9 

97 

>39-3 

J39-3 

57 

181.7 

181.7 

J3 

12.7 

12.7 

73 

55-2 

55-2 

3» 

97.6 

97.6 

98 

140.  o 

140.0 

58 

182.4 

182.4 

>9 

1-6-4- 

13-4 

79 

55-9 

55-9 

39 

9^-3 

98.3 

99 

140.7 

140.7 

59 

183.  i 

183.  i 

20 

1A.  I 

14-  I 

80 

56.6 

5&-6 

40 

99.0 

99-0 

200 

141.4 

141.4 

60 

183.8 

183.8 

ii 

14.  S 

14.8 

81 

57-3 

57-3 

141 

99-7 

99-7 

2O  I 

142.  i 

142.  i 

261 

184.6 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

42 

100.4 

100.4 

02 

142.8 

142.8 

62 

185-3 

185.3 

!3 

16.3 

16.3 

«3 

53.7 

53.7 

43 

101.  I 

I'M     I 

°3 

H3-5 

'43-5 

^3 

l£6.  o 

186.0 

24 

17.0 

17.0 

84 

59-4 

59-4 

44 

ioi.8 

101.8 

04 

144.2 

144.2 

64 

186.7 

186.7 

25 

«7-7 

«7-  7 

85 

60.  i 

60.  I 

45 

102.  5 

102.  S 

OS 

145.0 

145.0 

65 

187.4 

187.4 

25 

18.4 

18.4 

85 

60.8 

60.8 

46 

103.2 

IO3.  2 

06 

145-7 

145-7 

66 

iSS.  i 

183.  1 

27 

19.  i 

19.  i 

«7 

61.5 

61.5 

47 

>°3-9 

103.9 

°7 

146.4 

146.4 

67 

188.8 

iSS.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

48 

104.7 

104.7 

08 

147.1 

147-  ' 

68 

189.5 

189.5 

29 

20.5 

20.  5 

89 

62.  9 

62.9 

49 

105.4 

IOS.4 

09 

147.8 

147.8 

69 

190.2 

190.2 

go 

21.2 

21.2 

90 

63.6 

63.6 

5° 

106.  i 

ic5.  i 

10 

148.5 

148.5 

7° 

190.9 

190.9 

3' 

21.9 

21.9 

9i 

64-3 

64-3 

15' 

106.8 

106.8 

211 

149.2 

149.2 

271 

191.6 

191.6 

32 

32.6 

22.6 

92 

65.1 

65.1 

52 

107.5 

107.5 

12 

149.9 

149.9 

72 

192.3 

192.3 

33 
34 

23-3 
24.0 

23-3 
24.0 

93 
94 

65.8 
66.  5 

65.8 
66.5 

53 

54 

108.2 
108.9 

108.  2 
108.9 

13 

14 

150.6 
iSi-3 

150.6 
I5I-3 

73 
74 

193.0 
'93-7 

193.0 
193-7 

35 

24.7 

24.7 

95 

67.2 

67.2 

55 

109.6 

109.6 

«5 

152.0 

152.0 

75 

'94-5 

'94-5 

35 

25-5 

25-5 

96 

67.9 

67.9 

56 

110.3 

II0.3 

16 

152.7 

152.7 

76 

195.2 

195.2 

37 
3* 

26.2 
26.9 

26.2 
26.9 

9 

68.6 
69-3 

63.6 
69-3 

P 

1II.O 

111.7 

III.O 
III.7 

17 
18 

153-4 
154.  i 

153-4 
J54-I 

JZ 

>95-9 
196.6 

'95-9 
196.6 

33 

27.6 

27.6 

99 

70.  o 

70.0 

59 

112.4 

H2.4 

'9 

154-9 

154-9 

79 

197-3 

197-3 

43 

23.  .1 

28.3 

IOO 

70.7 

70.7 

60 

in.  i 

113.  I 

20 

'55-6 

'55-6 

80 

198.0 

198.0 

<I 

ij.0 

29.0 

101 

71.4 

71.4 

101 

113.8 

II3.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

2>7 

29.7 

02 

72.1- 

72.1 

62 

114.6 

II4.6 

22 

i57.o 

157.0 

82 

199-4 

199.4 

43 

3^-4 

33-4 

C3 

72.8 

72.8 

*3 

"5-3 

"5-3 

23 

»57.  7 

157-7 

83 

200.  I 

200.  i 

44 

3*-i 

3'-' 

04 

73-  S 

73-  S 

64 

116.  o 

no.  o 

24 

158.4 

158.4 

84 

200.8 

200.8 

45 

31.8 

31.8 

05 

74-2 

74.2 

€; 

116.  7 

116.  7 

25 

IS9-  J 

159.1 

85 

201.5 

201.5 

45 

32-5 

32-5 

06 

75-0 

75.0 

65 

117.4 

117.4 

26 

159-8 

159.8 

86 

202.2 

202.  2 

47 

33-2 

33-2 

«7 

75-7 

75-7 

67 

I  I'M 

118.  i 

27 

1  60.  5 

160.5 

87 

202.9 

202.9 

43 

33-9 

33-9 

08 

76.4 

76.4 

63 

II8.8 

liS.8 

28 

161.  2 

161.2 

88 

203.6 

203.6 

49 

34-6 

34-6 

09 

7M 

77-1 

69 

"9-3 

119.5 

29 

161.9 

161.9 

89 

204.4 

204.4 

50 

35-  A 

35-4 

10 

77-8 

77.8 

70 

120.2 

120.2 

30 

162.6 

162.6 

90 

205.  I 

205.  I 

£1 

36.1 

36.1 

in 

7^-5 

7*.  5' 

171 

1'20.  9 

120.9 

231 

»63-3 

163-3 

291 

205.8 

205.8 

52 

36.8 

36.8 

12 

79-2 

79-2 

72 

121.  6 

121.  6 

32 

164.0 

164.0 

92 

206.5 

206.  5 

53 

37-5 

3Z-S 

13 

79-9 

79-9 

73 

122.3 

122.3 

33 

164.8 

164.8 

93 

207.2 

207.2 

54 

P 

38.2 

38.9 
39-6 

38.2 

38.9 
39-6 

H 

IS 

16 

80.6 

81.3 
82.0 

£0.6 
81.3 

82..0 

74 
75 
76 

123.0 
'23-7 
124.5 

123.0 

123-7 
124.5 

34 

3 

165.5 
166.2 
166.9 

165.5 
166.2 
166.9 

94 

9 

207.9 
208.6 
209.3 

207.9 
208.6 
209.3 

57 

40-3 

40.3 

i? 

82.7 

82.7 

77 

I?5.2 

125-2 

37 

167.6 

167,6 

97 

2IO.  O 

2IO.  O 

58 

41.0 

41.0 

iS 

83-4 

83-4 

73 

I2;.  9 

"25-9 

38 

168.3 

168/3 

98 

210.  7 

210.7 

59 

41.7 

41.7 

19 

84.  i 

84.  1 

79 

126.6 

126.6 

39 

169.0 

169.0 

99 

2II.4 

211.4 

60 

42.4, 

20 

84-9 

84.9 

80 

IZ7-3 

127-  3 

40 

169.7 

169.7 

300 

212.  I 

212.  I 

Dist. 

Dep. 

Lat.   |  Dist. 

Dep. 

Let. 

Dlst 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

[For  45  Dep-ees. 

158 


TABLE  II. 

REFRACTION,   DIP,   AND  PARALLAX 


,    AINU 


^ 

4_3       . 

-O       • 

-«    • 

,    . 

~     rt" 

r-    CD 

r^    ^ 

fl  CD 

r-    CD 

0>T-j 

• 

®'2 

6  • 

g'O 

i 

O     • 

S-  D 

6  • 

Is 

o    • 

DIP  OP  THE  SEA 

|.l 

03  a 
£.2 

SJ 

03  S 

£.2 

EJ 

c3  £3 

£.2 

^1 

03  « 

03  P 

£.2 

HORIZON. 

0)  •*-> 

D  *J 

i.  — 

<3<1 

tf 

<^ 

03 

.t  <ri 
•^j 

M 

<  ^ 

PH 

^j*^ 
•^ 

Height 

Dip  of 

0           / 

/    // 

0       1 

/    // 

0       / 

/    // 

O       1            1      II 

O      / 

/  // 

of  the 

the  Ho- 

9 30 

5  35 

15    0 

3  34! 

25    0    2    4 

42    0 

1     5 

Eye. 

rizon. 

0    0 

36  29 

35 

5  32 

10 

3  32 

10    2    3 

20 

1     3 

1     0 

24  53 

40 

5  29 

20 

3  29 

20    2    2 

40 

1     3 

2    0 

18  25 

45 

5  27 

30 

3  27 

30    2    1 

43    0 

1     2 

Ft 

/    // 

3    0 

14  25 

50 

5  24 

40 

3  25! 

40    2    1 

20 

1     2 

1 

0  59 

4    0 

11  44 

55 

5  22 

50 

3  22 

50    2    0 

40 

1     1 

2 

1  23 

5    0 

9  52 

10    0 

5  19 

16    0 

3  20 

26    0    1  59 

44    0 

1     0 

3 

1  42 

5 

9  44 

5 

5  17 

10 

3  18 

10    1  58 

20 

0  59 

4 

1  58 

10 

9  36 

10 

5  14 

20 

3  16 

20    1  57 

40 

0  59 

5 

2  11 

15 

9  28 

15 

5  12 

30 

3  14 

30    1  56 

45    0 

0  58 

6 

2  24 

20 

9  21 

20 

5    9 

40 

3  12 

40    1  55 

20 

0  57 

7 

2  36 

25 

9  14 

25 

5    7 

50 

3  10 

50    1  54 

40 

0  57' 

8 

2  46 

5  30 

9    7 

10  30 

5    5 

17    0 

3    8 

27    0 

1  54 

46    0    0  56 

9 

2  56 

35 

9    0 

35 

5    2 

10 

3    6 

10 

1  53 

20    0  55 

10 

3  06 

40 

8  53 

40 

5    0 

20 

3    5 

20 

1  52 

40 

0  55 

11 

3  15 

45 

8  47 

45 

4  58 

30 

3    3 

30 

1  51! 

47    0 

0  54 

12 

3  24 

50 

8  46 

50 

4  56 

40 

3     1 

40 

1  51 

20 

0  54 

13 

1    t 

3  32 

*>        M  f\ 

55 

8  34 

55 

4  53 

50 

2  59 

50 

1  50 

40 

0  53 

14 

•j  40 

15 

3  48 

6    0 

8  28 

11    0 

4  51 

18    0 

2  57 

28    0 

1  49 

48    0 

0  52 

16 

3  55 

5 

8  22 

5 

4  49 

10 

2  56 

20 

1  48 

49    0 

9  50 

17 

4  02 

10 

8  16 

10 

4  47 

20 

2  54 

40 

1  46 

50    0 

0  49 

18 

T     v<*«* 

4  09 

15 

8  10 

15 

4  4-5 

30 

2  52 

29    0 

1  45 

51    0 

0  47 

19 

4  16 

20 

8    5 

20 

4  43 

40 

2  51 

20 

1  43 

52    0 

0  45 

20 

4  23 

25 

7  59 

25 

4  41 

50 

2  49 

40 

1  42 

53    0 

0  44 

21 

4  29 

6  30 

7  54 

11  30 

4  39! 

19    0 

2  48' 

30    0 

1  40 

54    0 

0  42 

22 

4  36 

35 

7  49 

•t? 

4  37 

10 

2    46; 

20 

1  39 

55    0 

0  41 

23 

4  42 

40 

7  43 

•±0 

4  35 

20 

2  45 

40 

1  38 

56    0 

0  39 

24 

4  48 

45 

7  38 

45 

4  33 

30 

2  43 

31     0 

1  37 

57    0 

0  37 

25 

4  54 

50 

7  33 

50 

4  31 

40 

2  42 

20 

1  35  J 

58    0 

0  36 

26 

5  00 

55 

7  28 

55 

4  29 

50 

2  40 

40 

1  34 

59    0 

0  35 

27 

5  06 

7    0 

7  24 

12    0 

4  27 

20    0 

2  39 

32    0 

1  33 

60    0 

0  33 

28 

5  11 

5 

7  19 

5 

4  26 

10 

2  37 

20 

1  32 

61     0 

0  32 

29 

5  17 

10 

7  14 

10 

4  24 

20 

2  36 

40 

1  31 

62    0 

0  31 

30 

5  22 

15 

7  10 

15 

4  22 

30 

2  35 

33    0 

OA 

1  29 

63    0 

0  30 

20 

7    6 

20 

4  20 

40 

2  33 

20 

1  2S 

64    0 

0  28 

25 

7    1 

25 

4  19 

50 

2  32 

40 

1  27 

65    0 

0  27 

THE  SUN'S  PAR- 

7 30 

6  57 

12  30 

4  17 

21     0 

2  31 

34    0 

1  26 

66    0 

0  26 

ALLAX  IN  ALTI- 

35 

6  53 

35 

4  15 

10 

2  29 

20 

1  25 

t)7    0 

0  25 

TUDE. 

40 

6  49 

40 

4  13 

20 

2  28 

40 

1  24 

68    0 

0  23 

45 

6  45 

45 

4  12 

30 

2  27 

35    0 

1  23 

69    0 

0  22 

50 

6  41 

50 

4  10 

40 

2  26 

20 

1  22 

70    0 

0  21 

Sun's 

Sun's 

55 

6  37 

55 

4    9 

50 

2  24 

40 

1  21 

71    0 

0  20 

Alt. 

Parallax. 

8    0 

6  33 

13    0 

4    7 

22    0 

2  23 

36    0 

1  20 

72    0 

0  19 

5 

6  2!) 

5 

4    5 

10 

2  22 

20 

1  19 

73    0 

0  18 

10 

6  25 

10 

4    4 

20 

2  21 

40 

1  18 

74    0    0  17 

D. 

S. 

6  22 

15 

4    2 

30 

2  20 

37    0 

1    17 

75     0    ft  i* 

20 

6  19 

*  •  i 

20 

4    1 

40 

(V       iVV7 

2  19 

20    1  16 

f  *J         \J 

76    0 

V        J  *J 

0  14 

25 

6  15 

25 

3  59 

50 

2  17 

40    1  15 

77    .0 

0  13 

0 

9 

8  30 

6  12 

13  30 

3  58 

23    0 

2  16 

38    0    i  14 

78    0 

0  12 

10 

Ctf\ 

9 

35 

6  s; 

35    3  56 

10 

2  15 

20    1  13 

79    0 

0  11 

20 

f)f\ 

40 

6    5 

40 

3  55 

20 

2  14 

40  !   1  12 

80    0 

0  10 

30 

7 

45 

6    2 

45 

3  54 

30 

2  13 

39    0    1  11 

81    0    0    91 

t/i 

t 

50 

5  59 

50 

3  52 

40 

2  12 

20    1  11 

82    0    0    8 

50 

fr  K 

55 

5  56 

55 

3  51 

50 

2  11 

40    1  10 

83    0    0    8 

55 
60 

4 

9    0 

5  52 

14    0 

3  49 

24    0 

2  10 

40    0    1    9 

84    0    0    6 

65 

4 

5 

5  49 

10 

3  47 

10 

2    9 

20'   1     8 

85    005 

70 

3 

10 

5  46 

20 

3  44 

20 

2    8 

40    1     8 

86    0    0    4 

75 

2 

15 

5  43 

30 

3  41 

30 

2    7 

41     0    1     7 

S7    0    0    3 

80 

2 

20 

5  4l 

40 

3  39 

40 

2    6 

20    1     6 

SS    0    0    2 

85 

1 

25 

5  38 

50 

3  36 

50 

2    5 

40 

1     5 

S!)     0    0     1 

90 

0 

9  30 

5  35 

15    0 

3  34 

25    0 

2    4 

42    0 

1     4 

90    0|  0    0 

160 


TABLE  III. 

DECLINATION  OF  THE  SUN, 
1886-1901. 


DECLINATION  OF  THE  SUN  FOR  THE   YEARS  1886,   1890,   1894,   1868. 


JAN. 

FEB. 

MAR. 

APRII,. 

MAY. 

JUNE. 

A 

0) 

c   . 

j-j 

a    . 

^ 

—  * 

O) 

c    • 

a 

01 

a    • 

£ 

a 

a  ,. 

^ 

<D 

o^ 

.3 

O  5 

«3 

-g 

*_> 

°3 

c| 

0  5 

•_ 

°i 

C  0 

SH  O 

d  o 

O 

?H  ° 

c5  ^ 

oj 

cJ  ^ 

0-02 

<c  — 

1*    Uj              ^""*    -  T*l 

X  ^Q 

z 

H-H     r+ 

0*  ri 

^^  .  r*| 

£,£; 

^C    r^ 

fl\  £7* 

-C 

Q 

Q~ 

Q 

Q 

Q 

^ 

Q 

G 

Q 

5 

Q 

5 

60 

0         / 

n 

0        / 

n 

o      / 

;/ 

0         / 

/ 

„ 

0         / 

n 

09 

aS 

Q 

O 

1 

22.59 

+13 

17.02 

+43 

7.30 

+57 

4.37 

+58 

15.08 

+45 

22.05 

+20 

1 

2 

22.54 

14    16.44 

44 

7.07 

57 

5.00 

58 

15.26 

45 

22.13 

19 

2 

3 

22.48 

15    16.27 

44 

6.44 

57 

5.23 

57 

15.44 

44 

22.20 

18 

3 

4 

22.42 

16    16.09      45 

6.21 

58 

5.46 

57 

16.01 

43 

22.28 

17 

4 

5 

22.35 

+17 

15  51 

+46 

5.58 

+58 

6.09 

+57 

16.18 

+43 

22.34 

+16 

5 

6 

22.28 

'  18    15.32 

46 

5.34 

58 

6.32 

57 

16.35 

42 

22  41 

15 

6 

7 

22.21 

19    15.14 

47 

5.11 

58 

6.54 

56 

16.52 

41 

22.47 

14 

7 

8 

22.13 

20    14.55 

48 

4.48 

58 

7.17 

56 

17.08 

41 

22.52 

13 

8 

9 

22.04 

22    14.35 

48 

4.24 

59 

7.39 

56 

17.25 

40 

22  57 

12 

9 

10 

21.55 

+23    14.16+49 

4.01 

+59 

8.01 

+55 

17.40 

+39 

23.02 

+11 

10 

11 

21.46 

24    13.56 

49 

3.37 

59 

8  23 

55 

17.56 

38 

23.06 

10 

11 

12 

21.36 

25    13.36     50 

3.14 

59 

8.45 

55 

18.11 

38 

23.10 

9 

12 

13 

21.26 

26    13.16!     51 

2.50 

59 

9.  or 

54 

18.26 

37 

23.14 

8 

13 

14 

21.16 

27    12.55      51 

2  26 

59 

9.29 

54 

18.40 

36 

23.17 

r* 
t 

14 

15 

21.05 

+28 

12.35+52 

2.03 

+59 

9.50 

+53 

18.55 

+35 

23.20 

+6 

15 

16 

20.53 

29    12.1? 

52 

1.39 

59 

10.12 

53 

19.09 

34 

23.22 

5 

16 

17 

20.42 

30    11.54 

53 

1.15 

59 

10  32 

53 

19  22 

34 

23  24 

4 

17 

18 

20.30 

31 

11.33 

53 

0.52 

59 

10.54 

52 

19  36 

33 

23.25 

3 

18 

19 

20.17 

32 

11.11 

53 

0.28 

59 

11.15 

52 

19.49 

32 

23.26 

2 

19 

20 

20.04 

+33 

10.50 

+54 

0.04 

+59 

11.35 

+51 

20.01 

+31 

23  27 

+1 

20 

21 

19.51 

34 

10.28 

54 

0.19 

59 

11.56 

51 

20.13 

30 

23.27 

0 

21 

22 

19.37 

35 

10.06 

55 

0.43 

59 

12.16 

50 

20.25 

29 

23.27 

-1 

22 

23 

19.23 

35 

9.44 

55 

1.07 

59 

12  36 

50 

20  37 

28 

23.26 

2 

23 

24 

19.09 

36 

9.22 

55 

1.30 

59 

12.56 

49 

20.48 

28 

23.25 

3 

24 

25 

18.54 

+37 

9.00 

+56 

1.54 

+59 

13  15 

+  49 

20  59 

+27 

23.24 

-4 

25 

26 

18.39 

38 

8.38 

56 

21 

rt 

59 

13.35 

48 

21.10 

26 

23.22 

5 

26 

27 

18.24 

39 

8.15 

56 

2.41 

59 

13.54 

48 

21.20 

25 

X'3.20 

6 

27 

28 

18.08 

40 

7.52 

57 

3.04 

58 

14.13 

47 

21.30 

24 

23.17 

7 

28 

29 

17.52 

41 

7.30 

57 

3.28 

58 

14  31 

46 

21.39 

23 

23.14 

8 

9 

30 

17.35 

+41 

3.51 

+58 

14.50 

+46 

21.48 

+22 

23.10 

-9 

bO 

31 

17.19 

42 

4.14 

58 

15.08 

45 

21.57 

21 

23.07 

10 

31 

32 

17.02 

43 

4.37 

58 

22.05 

20 

32 

162 


DECLINATION   OF  THE  SUN   FOR   THE  YEARS    1886,    1890,   1894,   1898. 


JULY. 

AUGUST. 

SEPT.             OCT. 

Nov. 

DEC. 

i 

i 

a 

2 

A 

a   .      — 

c  .. 

—  '     B   • 

-a 

= 

A 

i 

43 

o  •: 

C  3         - 

+3 

3 

°  = 

,  3 

C3 

c  -' 

5  3' 

til 

Sti2 

il 

it!  2    £55 

3J§ 

fB2 

£  'J2     ^  5 

8*1 

^r*   O 

SJM 

fcj 

Q 

Q" 

Q 

S"  « 

5 

Q        P^ 

Q 

°" 

O  ' 

^ 

02 

[ft 

£ 

Cj 

0         / 

If 

0         / 

// 

o 

/ 

// 

0         / 

n 

0         / 

// 

o      / 

// 

<S 

Q 

1 

23.07 

-JO 

17.59 

-38 

8.13 

-54 

3.16 

-58 

14.30 

-48 

21.51 

-23 

1 

2 

33.02 

11 

17.44 

39 

7.52 

55 

3.39 

58 

14.49 

47 

22.00 

22 

2 

3 

22-58 

12 

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DECLINATION   OF  THE  SUN  FOR  THE  YEARS  1887,  1891,  1895,  1899. 


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DECLINATION  OF  THE  SUN   FOR  THE  YEARS  1887,  1891,   1895,  1899. 


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DECLINATION  OF  THE  SUN  FOR  THE  YEARS  1888,  1892,  1896,  1900. 


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DECLINATION  OF  THE  SUN  FOR  THE  YEARS   1888,  1892,  1896,  1900. 


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22 

14.28     46 

3.32 

58 

8.02 

56 

18.10 

39 

23.12 

9 

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21.35 

23 

14.10     47 

3.09 

58 

8.25 

56    18.25 

38 

23.16 

8 

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13.51  -47 

2.46 

-58 

8.47 

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18.41 

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23.19 

r- 
—  I 

15 

16 

21.16 

25 

13.32     48 

2.23 

58 

9.09 

55 

18.56 

37 

23.21 

6 

16 

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21.06 

26 

13.13     48 

1.59 

58 

9.10 

55 

19.10 

36 

23.24 

5 

17 

18 

20.55 

27 

12.53     49 

1.36 

58 

9.53 

54 

19.24 

35 

23.25 

3 

18 

19 

20.44 

28 

12.34      49 

1.13 

58 

10.14 

54 

19.38 

34 

23.26 

2 

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20.33 

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12.14  -50 

0.50 

-58 

10.36 

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19.52 

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20 

21 

20.21 

29 

11.54      50 

0.26 

58 

10.57 

53 

20.05 

32 

23.27 

+0 

21 

22 

20.09 

30 

11.34     51 

0.03 

58 

11.18 

53 

20.18 

31 

23.27 

1 

22 

23 

19.57 

31 

11.13     51 

0.20 

58 

11.39 

52 

20.30 

31 

23.26 

2 

23 

24 

19.44 

32 

1053      52 

0. 

44 

58 

12.00 

52 

20.42     30 

23.25 

4 

24 

25 

19.31 

-33 

10.32-52 

1.07 

-58 

12.21 

-51 

20  64 

-29 

23.23 

+5 

25 

26 

19.18 

34 

10.11      52 

1. 

31 

58 

12.41 

51 

21.05 

28 

23.21 

6 

26 

27 

19.04 

34 

9.50     53 

1. 

54 

58 

13.02 

50 

21.16 

27 

23.18 

7 

27 

28 

18.50 

35 

9.29 

53 

2. 

17 

58 

13.22 

50 

21.27 

25 

23.15 

8 

28 

29 

18.36 

36 

9.07 

54 

2.41 

58 

13.42 

49 

21.37 

25 

23.12 

9 

29 

30 

18.21 

-37 

8.46 

-54 

3. 

04 

—58 

14.01 

-49 

21.46 

-24 

23.07 

-1-11 

30 

31 

18.07 

37 

8.24 

54 

3. 

27 

58 

14.21 

46 

21.56 

23 

23.03 

11 

31 

33 

17.51 

38 

8.02 

55 

14.40 

48 

22.58 

13 

32 

167 


DECLINATION  OF  THE  SUN  FOR  THE  YEARS  1889,  1893,  1897,  1901. 


JAN. 

FEB. 

MARCH. 

APRIL. 

MAY. 

JUNE. 

^ 

- 

A 

" 

<£> 

A 

^ 

G 

A 

0 

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16.57 

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7.23 

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4.44 

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15.13 

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22.07 

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1 

2 

22.53 

14 

16.40 

44 

7.00 

57 

5.07 

57 

15.31 

44 

22.15 

19 

2 

3 

22.47 

15 

16.22 

44 

6.37 

58  1     5.30 

57 

15.49 

44 

22.22 

18 

3 

4 

22.40 

16 

16.04 

45 

6.14 

58 

5.53 

57 

16.06 

43 

22.30      17 

4 

5 

22.34 

+17 

15.46 

+46 

5.51 

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6.15 

+57 

16.23 

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22.36  +16 

5 

6 

22.26 

19 

15.27 

47 

5.28 

58 

6.38 

56 

16.40 

42 

22.42 

15 

6 

7 

22.19 

20 

15.08 

47 

5.05 

58 

7.01 

56 

16.57 

41 

22.48      14 

7 

8 

22.11 

21 

14.49 

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4.41 

58 

7.23 

56 

17.13 

40 

22.54      13 

8 

9 

22.02 

22 

14.30 

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4.18 

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7.45 

56 

17.29 

40 

22.59 

12 

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10 

21.53 

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14.11 

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3.54 

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8.08 

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17.45 

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23.03+11 

10 

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21.44 

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13.51 

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3.31 

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8.30 

55 

18.00 

38 

23.07 

10 

11 

12 

21.34 

25 

13.31 

50 

3.07 

59 

8.51 

54 

18.15 

37 

23.11 

9 

12 

13 

21.24 

26 

13.11 

51 

2.43 

59 

9.13 

54 

18.30 

37 

23.15 

8 

13 

14 

21.13 

27 

12.50 

51 

2.20 

59 

9.35 

54 

18.44 

36 

23.18 

7 

14 

15 

21.02 

+28 

12.30 

+52 

1.56 

459 

9.56 

+53 

18.59 

+35 

23.20 

+6 

15 

16 

20.50 

29 

12.09 

52 

1.32 

59 

10.17 

53 

19.12 

31 

23.22 

5 

16 

17 

20.38 

30 

11.48 

53 

1.09 

59 

10.39 

52 

19.26 

33 

23.24 

4 

17 

18 

20.26 

31 

11.27 

53 

0.45 

59 

10.59 

52 

19.39 

33 

23.26 

3 

18 

19 

20.14 

32 

11.05 

54 

0.2 

I 

59 

11.20 

52 

19.52 

32 

23.26 

2 

19 

20 

20.01 

+33 

10.44 

+54 

0.02 

+59 

11.41 

+51 

20.05 

+31 

23.27 

+1 

20 

21 

19.47 

34 

10.22 

54 

0.26 

59 

12.01 

51 

20.17 

30 

23.27 

-0 

21 

22 

19.33 

35 

10.00 

55 

0.49 

59 

12.21 

50 

20.29 

29 

23.27 

1 

22 

23 

19.19 

36 

9.38 

55 

1.13 

59 

12.41 

50 

20.40 

28 

23.26 

2 

23 

24 

19.05 

37 

9.16 

56 

1.37 

59 

13.01 

49 

20.51 

27 

23.25 

3 

24 

25 

18.50 

+37 

8.54+56 

2.00 

+59 

13.21 

+49 

21.02 

+26 

23.23 

-4 

25 

26 

18.35 

38 

8.31 

56 

2.24 

59 

13.40 

48 

21.12 

26 

23.21 

5 

26 

27 

18.19 

39 

8.09     57 

2.47 

59    13.59 

47 

21.23 

25 

23.19 

6 

27 

28 

18.03 

40 

7.46 

57 

3.11 

58    14.18 

47 

21.32 

24 

23.16 

7 

28 

29 

17.47 

41 

7.23 

57 

3.34 

58 

14.36 

46 

21.42 

23 

23.13 

8 

29 

30 

17.31 

+42 

3.57 

+58 

14.55 

+46 

21.51 

+22 

23.09 

-9 

30 

31 

17.14 

42 

4.21 

58 

15.13 

45 

21.59 

21 

23.05 

10 

31 

32 

16.57 

43 

4.44 

581 

22.07 

20 

32 

i 

i 

1 

168 


DECLINATION    OF    THE   SUN    FOR   THE    YFAKS    1889,  1893,  1897,  1901. 


JULY. 

AUG. 

SEPT. 

OCT. 

Nov. 

DEC. 

J3 

D 
a 

a 

£ 

^ 

a 

D 
C     • 

f.       O     • 

•    ;  ® 

.c     ~    • 

-e 

•t* 

3  -' 

•W 

«j      G  «- 

**     c  - 

5    c  j-' 

C     c  «- 

M 

fei  ® 

ag. 

3 

•  o 

0      fe    = 

y     C           '{H      C 

d  c     SH  c 

d  c    £  o 

0^  ^H 

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U  ^H 

•  «  -^ 

I/  i^i 

72 

•  «     — 

i,  V       .S  » 

IX      ~  J3 

Q 

ft 

Q 

Q 

ft 

Q 

o 

- 

Q 

ft 

Q*       Q- 

09 

ti 

0         / 

H 

0         / 

o      / 

n 

0         / 

// 

O          / 

0         / 

fl 

m 

0 

ft 

1 

23.06 

-11 

17.55 

-38 

8  07 

-55 

3.22 

—58 

14.35 

-48 

21.54 

-23 

1 

2 

23.01 

12 

17.40 

39 

7.46 

55 

3.45 

58 

14.54 

47 

22.02 

22 

2 

3 

22.56 

13 

17.24 

39 

7.24 

55 

4  08 

58 

15.13 

47 

22.11 

21 

3 

4 

22  51 

16 

17.  OS 

40 

7.01 

55 

4  31 

58 

15.32 

46 

22.19 

20 

4 

5 

22.45 

-15 

16.52 

-41 

6.39 

-56 

4.55 

-58 

15.50 

-45 

22.27 

-18 

5 

6 

22.39 

16 

16.35 

41 

6.1 

7 

56 

5.18 

57 

16.08 

45 

22.34 

17 

6 

7 

22.33 

17 

16.19 

42 

5.54 

56 

5.41      57 

16.26 

44 

22.41 

16 

r* 
t 

8 

22.26 

18 

16.01 

43 

5.32 

56 

6.04      57 

16.43 

43 

22.47 

15 

8 

9 

22.19 

19 

15.44 

43 

5.09 

57 

6.26      57 

17.00 

43 

22.53 

14 

9 

10 

22.12 

-20 

15.27 

-44 

4.46 

-57 

6.49  -57 

17.17 

-42 

22.58 

-13 

10 

11 

22.04 

20 

15.09 

45 

4.23 

57 

7.12      56 

17.34 

41 

23.03 

12 

11 

12 

21.55 

2! 

14  51 

45 

4.01 

57 

7.34      56 

17.50 

40 

23.07 

11 

12 

13 

21.47 

22 

14.33 

46 

3.38 

57 

7.57 

56 

18.06 

39 

23.12 

10 

13 

14 

21.38 

23 

14.14 

46 

3.15 

58 

8.19 

56 

18.22 

39 

23.15 

8 

14 

15 

21.28 

-24 

13.54 

-47 

2.51 

-58 

8.41 

—55 

18.37 

-38 

23.18 

^ 

15 

16 

21.18 

25 

13.37 

48 

2.28 

58 

9.04      55 

18.52 

37 

23.21 

6 

16 

17      21.08 

26 

13.17 

48 

2.05 

58 

9.26      55 

19.07      36 

23.23 

5 

17 

18 

20.58 

27 

12.58 

49 

1.42 

58 

9.47      54 

19.211     35 

23.25 

4 

18 

19      20.47 

28 

12  38 

49 

1.19 

58 

10.09 

54 

19.35     34 

23  .  26 

2 

19 

20     20.36 

-28 

12.19 

-50 

0.55 

-58 

10.31 

-54 

19.49  -34 

23.27 

-1 

20 

21      20  24 

29 

11.59 

50 

0.32 

58 

10.52 

53 

20  02 

33 

23.27 

0 

21 

22      2012 

30 

11.39 

51 

0.08 

58 

11.13      53 

20.15 

32    23.27 

+1 

22 

23      20  00 

31 

11.18 

51 

0.15 

58 

11.34      52 

20.27 

31    23.26 

2 

23 

24      19.47 

31 

10.58 

51      0.38 

58 

11.55      52 

20.40 

30 

23.25 

3 

24 

25      19.34 

-33 

10.37 

-52      1.02 

-58 

12.16  -51 

20.51 

-29 

23  24 

+5 

25 

26      19.21 

33 

10.16 

52      1.25 

58 

12.37 

51 

21.03 

28 

23.22 

6 

26 

27 

19.08 

34 

9.55 

53      1.48 

58 

12.57      51 

21.14      27 

23.19 

7 

27 

28 

18.54 

35 

9.34 

53      2.12 

58 

13.17      50 

21.241     26 

23  16 

8 

28 

29 

18.39 

36 

9.12 

53     2.35 

58 

13.37      49 

21.34 

25 

23.12        9 

29 

30 

18.25 

-37 

8.51 

-54,     2.58 

-58 

13.57 

-49 

21.44 

-24 

23.09 

+10 

30 

31 

18.10 

37 

8.29 

54 

3.27 

58 

14.16 

48 

21.53 

23 

23.04 

12 

31 

32 

17.55 

38 

8.08 

55 

14.35 

48 

22.59 

13 

32 

169 


TABLE  IV. 

EQUATION  OF  TIME, 
1886-1901. 


EQUATION  OF  TIME  FOR  THE  YEARS   1886,  1890,  1894,  1898. 


JAN. 

FEB. 

MAR. 

APR. 

MAY. 

JUNE. 

JULY 

AUG. 

SEPT. 

OCT. 

Nov. 

DEC. 

o5 

03 

<D 

<B 

i 

6 

<D 

« 

a/' 

oi 

0) 

0) 

S 

a 

a 

aa 

a    a 

a 

a 

aa 

as 

as 

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O  *r^ 

O  T^ 

O        '£ 

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0 

0     . 

o*t 

o  i   . 

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o  . 

o   . 

«M 

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f— 

2 

43  a 

C-, 

43  a 

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*•"  a 

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^  a 

.  a 

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73  ^ 

73  a 

73  a 

73  a 

73    J3   & 

fi  a 

j$  73  a  73  a 

73  a 

,c  a 

,d  a 

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pO 

73    ~ 

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73  08 

3  c3 

3   73  S3 

73  eg 

73  oj 

3  s3 

3    fly 

p 

J"j    c3 

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<:  CO 

co 

CO   <J 

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50 

CO 

CO 

CO 

00 

0 

M.  S 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.S. 

M.  S. 

1 

353 

1351 

1230 

354 

302 

227 

333 

605 

008 

1021 

1618 

1044 

2 

421 

1358 

1218 

336 

310 

218 

344 

601 

027 

1040 

16  18 

1021 

3 

449 

1405 

1205 

318     316 

208 

355 

557 

046 

1058 

1618 

958 

4 

5  16 

1410 

11  52 

300 

322 

158 

406 

552 

105 

11  17 

1618 

933 

5 

543 

1415 

1138 

243 

327 

147 

417 

546 

125 

1135 

1616 

909 

6 

610 

1420 

1124 

225 

332 

137 

427 

540 

1  45 

11  52 

1614 

843 

7 

636 

1423 

11  10 

208 

337 

1  26 

437 

533 

205 

1209 

1610 

818 

8 

702 

1425 

1055 

1  51 

341 

1  14 

447 

525 

226 

1226 

1606 

r 

"51 

9 

727 

1427 

1040 

1  34 

344 

1  03 

456 

517 

246 

1242 

1602 

725 

10 

751 

1428 

1025 

1  18 

346 

051 

504 

509 

307 

1258 

1556 

657 

11 

815 

1428 

1009 

1  02 

349 

039 

513 

459 

328 

1314 

1549 

630 

12 

838 

1427 

953 

046 

350 

027 

520 

449 

349 

1329 

1542 

602 

13 

901 

1426 

936 

030 

351 

0  15 

528 

439 

410 

1343 

1534 

534 

14 

923 

1424 

919 

015 

351 

002 

534 

428 

431 

135? 

1525 

505 

15 

944 

1421 

902 

000 

351 

010 

541 

417 

452 

1411 

1515 

436 

16 

1005 

1417 

845 

015 

351 

023 

546 

405 

314 

1424 

1504 

407 

17 

1024 

1413 

827 

029 

349 

036 

552 

352 

535 

1436 

1452 

338 

18  10  44 

1407 

810 

043 

348 

049 

557 

339 

556 

1447 

1440 

308 

19   11  02 

1402 

752 

057 

345 

102 

601 

326 

617 

1458 

1426 

238 

20   11  20 

1355 

734 

1  10 

342 

1  14 

604 

312 

638 

1509 

1412 

209 

21 

11  37 

1348 

715 

1  22 

339 

1"27 

608 

257 

659 

1518 

1357 

] 

[39 

22 

11  53 

1340 

657 

1  35 

335 

1  40 

610 

242 

720 

1527 

1341 

] 

109 

23 

1208 

13  33 

639 

147 

330 

1  53 

612 

227 

741 

15  36 

1324 

038 

24 

12  23 

1323 

620 

1  58 

325 

206 

614 

211 

802 

1543 

13  07 

0 

08 

25 

1236 

1313 

602 

209 

320 

219 

615 

155 

822 

1550 

1249 

022 

26 

1249 

1303 

543 

219 

314 

232 

615 

1  39 

843 

1556 

1230 

051 

27 

1302 

1253 

525 

229 

307 

244 

6  15 

1  22 

903 

1602 

1210 

] 

.21 

28 

1313 

1242 

507 

238 

300 

257 

614 

1  04 

923 

1607 

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0*0*0*0* 

ojo*  co  co 

COCO  CO  CO 

Tr^^^ 

5   CO 

000^ 

^^^^ 

^~~0» 

0*0*0*0* 

ojo*  ojco 

CO  CO  CO  CO 

i    OJ 

oooo 

nO*O*  O* 

7iO?C7^ 

^   1-1 

oooo 

oooo 

•anon 

~OJ«^ 

mot-  oo 

OSOnOJ 
11  1—  1  11 

CO  TT  1C  CO 

t-oocso 

-lOICO  Tf 

0*0*  0*0* 

176 


TABLE  V. 

SINES,    TANGENTS,    AND  SECANTS. 


SINES.  TANGENTS.  AND  SECANTS. 
0° 

179= 

M. 

[our  A.  «. 

lour  p.  M. 

Sine. 

Diff.  »'. 

Cosecant. 

Tangent. 

DiQ.  i  . 

Cotangent. 

Secant. 

Cosine. 

M. 

0 

I 

2 

3 

4 

200 
I    59  S2 
59  44 
59  36 
59  aS 

O      O      O 

o    8 
o  16 
o  24 

o  32 

nf.  neg. 

6.40373 
76476 
94085 
7.06579 

30103 
17609 
12494 
9691 

Infinite. 
.3-53b27 
23524 
05915 
[2.93421 

Inf.  neg. 

6.46373 
76476 
94085 
7-  °6579 

30103 
17609 
12494 
9691 

Infinite. 
3-  53627 
235=4 
05915 
2.93421 

0.  OOOOO 

ooooo 
ooooo 
ooooo 
ooooo 

o.  ooooo 
ooooo 
ooooo 
ooooo 
ooooo 

60 

59 

58 
57 

56 

8 
9 

I  59  20 
59  12 

59    4 
58  56 

58  4S 

o    o  40 

0   48 

o  56 
4 

12 

7.  16270 
24188 
-    ggj 

36682 
4'797 

7918 
6694 
5800 

5"5 

4576 

12.83730 
75812 
69118 
63318 
58203 

7.  16270 
24188 
v  H  ^ 
36682 

41797 

7918 
6694 
5800 

5"! 
4576 

2.83730 
75812 
'  jn8 
63318 

5$203 

c  .  c  :  :  ~-j 
ooooo 
ooooo' 
ooooo 
ooooo 

o.  ooooo 
ooooo 
ooooo 
ooooo 
ooooo 

53 

54 

53 
52 
51 

10 

II 

12 

'3 
H 

I  58  40 

58  32 
58  24 
58  16 
58    8 

0            20 
28 

36 

44 

52 

7-46373 
50512 

54291 

57767 
60985 

4i39 
3779 
347o 
3218 
2997 

12.53027 
49488 

457°9 
42233 
39°  '5 

7-46373 
50512 
54291 

57/67 
60986 

4139 

3779- 
3476 

3219 
2996 

2.  SS6^? 
49488 

457°9 
42233 

39°  1  4 

o.  ooooo 
ooooo 
ooooo 
ooooo 
ooooo 

o.  ooooo 
ooooo 
ooooo 
ooooo 

DC  3OO 

5" 

49 
48 
47 
46 

'5 
16 

17 

iS 
19 

I   58     o 
57  52 
57  44 
57  36 

57  28 

020 

2      8 

2  16 

2    24 
2    32 

7.  63982 
66784 
69417 
71900 

74248 

2802 
2633 
2483 
234* 
2227 

12.  36018 
33216 

3°5S3 
28100 

25752 

7-  63982 
66785 
69418 
71900 
74248 

2803 
2633 
2482 
2348 
2228 

2.  36018 

33215 
30582 
28100 

25752 

IO.  ooooo 
ooooo 

00001 
OOOOI 
OOOOI 

o.  ooooo 
ooooo 
9-99999 

99999 
99999_ 

45 
44 
43 

I 

20 

21 
22 
23 

24 

ii  57  20 
57  >2 
57    4 

5^5« 
56  4S 

0      2   40 
2    48 
2    56 

3    4 

3    '2 

7-  76475 
78594 
80615 
82545 
84393 

2119 

2021 

1930 
1848 

1773 

12.23525 
21406 
I93S5 
1/455 
15607 

7-  764/6 

"8595 
80615 
82546 
S4394 

2119 

2O2O 

1931 
1848 

«773 

2.23524 
21405 

'9385 
17454 
15606 

IO.  OOOOI 
OOOOI 
OOOOI 
OOOOI 

OOOOI 

9.99999 
99999 

99999 
99999 

99999 

40 

P 
\ 

25 
20 

27 

28 

29 

ii  56  40 

S6,  32 
56  24 

56  r6 

56    8 

o     3  20 

31 

3  36 
3  44 
3  52 

7.86166 
87870 
89509 
o^oSS 
52612 

1704 

'639 

1579 
1524 
1472 

2-  13834 

12130 

10491 

08012 

07325 

-.  86167 
87871 
89510 
91089 
92613 

1704 
1639 

'579 

1524 

H73 

2.  I3S33 
12129 
10490 
08911 

0/3S7 

10.  OOOOI 
OOOOI 
OOOOI 
OOOOI 
O0002 

9.99999 
999    , 
99999 
99999 
9999s 

35 
34 
33 

32 
31 

3° 
3' 
32  ' 
33 
S4 

ii   s6     o 

55  52 
55  44 
55  36 

55  28 

040 
4    8 
4  16 
4  24 
4  S2 

7-  94084 
95508 
96887 
98223 
99520 

1424 
1379 
1336 
1297 
1259 

12.05916 

04492 

03113 
01777 

00480 

7.94086 
95510 
96889 
98225 
99522 

1424 
1379 
1336 
1297 
1259 

12.05914 
04490 
03III 

01775 
00478 

IO.  OOO02 
OOOO2 
oAo02 
O0002 
00002 

9-  99993 
99998 

9999s 
99993 

9999s 

3° 
29 
28 

27 
26 

35 
36 

P 

39 

ii  55  20 
55  12 
55    4 
54  56 

54  4§ 

o     4  40 
448 
4  56 

5    4 

5  I2 

8.00779 

O2OO2 
03192 

°435° 
05478 

I223 
II9O 
II5S 
1128 
IIOO 

11.99221 

97998 
96808 
95650 

94522 

8.  oo-Si 
02004 
03194 

°4353 

05481 

1223 
1190 
1159 
1128 

IIOO 

11.99219 
97996 
96806 

95647 
94519 

IO.  OOOO2 
OOOO2 

00003 
00003 

00003 

9.  9999^ 
9999s 
99997 
99S97 
99997 

25 
24 
23 

22 
21 

4° 
4' 
42 

43 
44 

II   54  40 
54  32 
54  24 
54  16 
54    8 

o    5  20 

S2? 

5  36 

5  44 

5  S2 

S.  065  78 
07650 
08696 
09718 

10717 

1072 
1046 

IO22 

999 
976 

11.93422 
9235° 

9I3°4 
90282 
89283 

8.  06501 

07653 

c  ?  7  .  . 
09722 
10720 

1072 
1047 

1022 
998 
976 

H-934'9 
92347 
9«3°P 
90278 
89280 

10.  00003 
00003 
00003 
00003 
00004 

9-  99997 
99997 
99997 
99997 
99996 

20 
19 

18 

17 

16 

45 
46 

47 
4S 

49 

II  54     o 
53  52 
53  44 
53  36 
53  28 

060 
6    8 
6  16 
6  24 

6  32 

8.  11693 
12647 
I358i 
14495 
I539I 

954 
934 
9H 
896 

877 

ii.  08307 

87353 
86419 

85505 

84609 

8.  11696 
12651 

13585 
14500 

'5395 

955 
934 
9«5 
895 
878 

II.  88304 

87349 
86415 
85500 
84605 

10.00004 
00004 
00004 
00004 
00004 

9.99996 
99996 
99996 
99996 
90996 

'5 
M 
13 

12 
II 

5° 
M 
52 
53 
54 

ii  53  20 
53  " 

53    i 

52  56 

S2  48 

o     6  40 
648 
6  56 
7    4 
7  12 

S.  16268 
17128 

1/971 
18798 
19610 

860 

843 
827 

Sl2 

797 

11.83732 
82872 
82029 
81202 
80390 

8.  16273 

I7I33 
17976 
18804 

19616 

S6o 

843 
828 
812 

797 

11.83727 
82867 
&202J 
81196 
80384 

lo.  00005 
00005 
00005 
00005 
00005 

99995 
99995 
99995 
99995 
99995 

10 
I 

I 

55 
56 
57 
5» 
59 
60 

ii  52  40 
52  S2 
52  24 
52  16 
52    8 
52    o 

0      7   20 

728 
7  36 
7  44 

1*0 

8.  20407 
21189 
21958 
2-713 
23456 
24186 

702 
769 
755 
743 
73° 
7'7 

i  ;  .  ;  -  :  . 
78811 
78042 
77287 

76544 

75814 

8.20413 
21195 
21964 
22720 
23462 
24192 

782 
769 
750 
742 
730 
718 

II.795S7 
78805 
78036 
77280 

76538 
75808 

10.00006 
00006 
00006 
00006 
00006 
oooc  7 

9-99994 
99994 
99994 
99994 
99994 
99993 

i 

4 
3 

2 
I 
0 

M 

Hour  r.  « 

Hour  A.  x 

Cosine. 

Diff.  i' 

Secant. 

Cotangent 

Difl.  i' 

Tangent 

Cosecant. 

Sine. 

M. 

SXP                                                                                                                                                            89° 

178 


SINES,  TANGENTS,  AND  SECANTS. 
1°                                                                                                                                           ITS0 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff.  i'. 

Cosecant. 

Tangent. 

Diff.  i'. 

Cotangent 

Secant. 

Cosine. 

M. 

O 

I 

2 

3 

4 

II   52     0 
SI   52 
51   44 
5'  36 

51  28 

080 

8    .8 

8  16 
8  24 
832 

8.24186 

249°3 
25609 
26304 
26^88 

71I 
706 

695 
684 

673 

11.75814 
75°97 
74391 
73696 
73012 

8.  24191 
24910 
25616 
26312 

26996 

718 
706 
696 
684 
673 

II.7S8oS 
75090 

74384 
73688 

73004 

10.  00007 
00007 
00007 
00007 
ooooS 

9-99993 
97993 
99993 
99993 
99992 

'• 
59 
5* 
57 
56 

6 

8 
9 

II    51    20 
51    12 

51  1 

50  56 

50  48 

o    8  40 
8  48 
8  56 

9    4 
9  12 

8.27661 
28324 
28977 
29621 

30255 

663 
653 
644 
634 
624 

11.72339 
71676 
71023 
70379 
69745 

8.  2-669 

28332 
28986 
29629 
30263 

663 
654 
643 
634 
625 

H.  72331 

71668 
71014 
70371 

<-">:.;  7 

IO.  00008 
ooooS 
00008 
ooooS 
00009 

9-  99992 
99992 
99992 

99992 
99991 

55 
54 
53 

5- 
5' 

10 

ii 

12 

'3 
14 

11  50  40 

5°  32 
50  24 
50  16 
50    8 

o    9  20 
9  2& 
9  36 
9  44 
9  52 

8.  30879 
3  '495 
32103 

32702 

33-92 

616 
608 

599 
590 

533 

11.69121 
68505 

67897 
67298 
66708 

8.30888 

3  '5°5 
32112 
32711 
33302 

617 
607 
599 
59i 
584 

11.69112 

68495 
67888 
67289 
66698 

10.  00009 
00009 

OOOIO 
OOOIO 
OOOIO 

9-  99991 
99991 

99990 
99990 

2222; 

5° 

49 
4* 
47 
46 

15 
1  6 

17 
18 

>9 

II  50    o 
49  52 
49  44 
49  36 
49  28 

0    IO      O 

10    8 
10  16 
10  24 
10  32 

8.33875 
34-150 
35018 
35578 
3613' 

III 
560 

553 
.547 

11.66125 

65550 
64982 
64422 
63869 

8.  33886 
34461 
35029 
35590 
36143 

575 
&S 
561 

553 
546 

11.66114 

65539 
64971 
64410 
63857 

10.  OOOIO 

oooil 

OOOII 
OOOII 
OOOII 

\-  '  • 
99989 
99989 

99989 
99989 

45 
44 
43 
42 
41 

20 

21 

22 
23 

24 

II  49  20 
49  '2 

49     4 
48  56 

48  48 

o  10  40 
10  48 
10  56 
ii     4 

II    12 

8.  36678 
37217 
37750 
38276 

38796 

539 
533 
526 
520 
5H 

11.63322 

62783 
62250 
61724 

61204 

8.  36689 
37229 
37762 
38289 

38809 

540 
533 
5*7 
520 

5'4 

11.63341 
62771 
62238 
61711 
61191 

IO.  OOOI2 
OOOI2 
OOOI2 

00013 

00013 

9-  99988 
99088 
99988 
99987 
99987 

40 
39 
38 

11 

25 
26 
27 
28 
29 

ii  48  40 

48  32 
48  24 
48  16 
48     8 

0    II    20 
II    28 
II    36 

ii  44 
n  52 

8-  393'° 
39818 
40320 
40816 
41307 

508 
502 
196 

KM 

485 

11.60690 
60182 
59680 
59184 
58693 

8-  39323 
39832 
40334 
40830 

41321 

509 
502 
496 
491 
486 

11.60677 
60168 
59666 

5917° 
58679 

10.  00013 
00014 
00014 
00014 

0001^ 

9.  99987 
99986 
99986 
99986 
99985 

35 

34 
33 
32 
31 

3° 
3' 
32 
33 

34 

II  48     o 
47  52 
47  44 
47  36 
47  28 

O    12      0 
12      8 
12    16 
12   24 
12   32 

8.41792 
42272 
42746 
43216 

43680 

480 

474 
470 
464 
459 

n.  5^208 
57728 
5/254 
56/84 
56320 

8.41807 
42287 
42762 

43232 
43696 

480 

475 
470 
464 
460 

11.58193 

57713 
57238 
56768 
56304 

10.  00015 
00015 
txx>i6 
00016 
00016 

9.99985 
99985 
99934 
99984 
99984 

3° 
29 
28 

11 

35 
36 

9 

39 

H  47  20 
47  12 
47    4 
46  56 
46  48 

0    12   40 
12   48 
12   56 

13     4 
13    12 

8.44139 

44594 
45044 

45489 
4593° 

455 
450 

445 
441 

436 

11.55861 
55406 
54956 
545" 

54070 

8.44156" 
44611. 
45061 
45507 

4594S 

455 
450 
446 
441 

437 

11.55844 
55389 

54939 
54493 
54052 

10.  00017 
00017 
00017 
00018 
oooiS 

9-  999S3 
99983 

999S3 
99982 
99982 

25 
24 

23 

22 
21 

40 

4' 
42 
43 

44 

ii  46  40 
46  32 
46  24 

46    ID 

46    8 

a  13  20 
13  28 
'3  30 
13  44 
13  52 

8.  46366 
46799 
47226 
47650 

433 
427 
424 
419 

416 

H-S3634 
53201 

52774 
5?35o 
5'93i 

8.  46385 
46817 

47245 
47669 
48089 

432 
428 
424 
420 
4l£ 

"•536i5 
53  '«3 
52755 
52331 
51911 

10.  00018 
00619 
00019 
00019 

OOO2O 

o.  99982 
99981 

99901 
99981 
90980 

IO 
19 

IS 

17 
16 

45 
46 

47 
48 

49 

II    46      0 

45  52 
45  44 
45  36 
45  28 

o  14    o 
14    8 
14  16 
14  24 
14  32 

8.  48485" 
48896 

493°4 
49708 
50108 

411 

408 
404 
400 
396 

"•51515 
51104 
50696 
50292 
49892 

8.  48505 
48917 
49325 
49/29 
50139 

412 

408 

404 
401 

397 

11.51495 
51083 

50675 
50271 
49870 

IO.  COD2O 
OOO2I 
OOO2I 
OOO2I 
OOO22 

9.99980 
99979 
99979 
99979 

0:107$ 

'5 
14 
13 

12 
11 

Su 
51 
•S2 
53 

54 

ii  45  20 
45   12 
45     4 
44  5s 
44  48 

o  14  40 
14  48 
14  56 
15    4 

I5    12 

8.  5°5°4 
50897 
51287 
51673 
52055 

393 

$ 

370 

11.49496 
49103 
48713 
48327 
47945 

8.  50527 
50920 
5'3io 
51696 
52079 

393 
39o 
386 

3!3 
380 

H-49473 
49080 
48690 
48304 
47921 

IO.  OOO22 
ODO23 
OO023 
OO023 
OOO24 

9-  99978 
99977 
99977 
99977 
99976 

]  :• 
6 

55 

5° 

P 

59 
60 

II  44  40 

44  32 
44  24 

44  16 
44    8 
44    o 

0    15    20 
15    28 
15    36 

15  44 
15  52 
16    o 

8.  52434 
52810 

53183 
53552 
539'9 
54282 

375~ 
373 
369 
367 
363 
360 

11.47566 
47190 
46817 
46448 
46081 
457i8 

8.  52459 

52835 
53208 

53573 
53945 
543°8 

376 

373 
370 
367 

3<3 
361 

».4754« 
47165 
46792 
46422 

46055 
45692 

10.  00024 

00025 
OO025 
OOO25 

00026 
00026 

9-  99976 
99975 
99975 
99974 
99974 
99974 

5 
4 
3 

2 
I 
O 

M. 

Hour  P.  M. 

Hour  A.  M. 

Cosine. 

Diff.  i'. 

Secant. 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant 

Sine. 

M. 

91° 

88° 

179 


s° 

SINES,  TANGENTS,  AND  SECANTS. 

177° 

M. 

Hoia1  A.  M. 

Hour  P.*I. 

Sine. 

Di£  i'. 

Cosecant. 

Tangent 

Diff.  i'. 

Cotangent. 

Secant 

Cosine 

M. 

0 

i 

2 

3 
4 

II  44  o 

43  52 
43  44 
43  36 
43  23 

O  10   O' 

16  8 
16  16 
16  24 

16  32 

8.  54282 
54642 
54999 
55354 
55705 

360 
357 
355 
35' 

349 

11.45718 
45358 
45001 
44646 

44295 

8.  54308 
54669 

55027 
55382 
55734 

36, 
358 

355 
352 
349 

1  1.  45692 
4533' 
44973 
44610 
44266 

lo.  00026 
00027 
00027 
00028 
00028 

9  09974 
99973 
99973 
99972 
99972 

60 

52 
5« 

57 
S6 

1 
I 

9 

ii  43  20 
43  12 
43  4 
42  56 

42  48 

o  16  40 
16  48 
16  56 
17  4 

17  12 

8.  56054 
56400 

56743 
57084 

57421 

346 
343 
341 
337 
336 

11.43946 

43600 

43257 
42916 

42579 

8.  56083 
56429 
56773 
57"4 
57452 

346 
344 
341 
338 
3^6 

11.43917 

43571 
43227 
42885 
42548 

10.  00029 
00029 
00030 
00030 
__  00031 

9.99971 

99971 
99970 
99970 

99969 

55 
54 
53 
52 
5' 

10 

ii 

12 
13 

'4 

ii  42  40 

42  S3 
42  24 

42  1  6 
42  8 

0  17  20' 
17  28 
1736 

17  44 
17  52 

8-57757 
58089 

584i9 
58747 
59072 

332 
330 
328 
325 
323 

11.42243 
41911 
4I58I 
41253 
40928 

8.57788 
58121 

58451 
58779 
59>o5 

333 
33° 
328 
326 
323 

11.45212 
41879 

41549 
41221 
40895 

10.  00031 

00032 

00032 

00033 

OOO31 

9.  99969 
99968 
99968 

99967 
99967 

So 
49 
48 
47 
46 

15 
16 

17 
18 

19 

ii  42  o 

41  52 
41  44 

41  36 
41  28 

o  18  o 
18  8 
i3  16 
18  24 
18  32 

8.  59395 
59715 
60033 
60349 
60662 

320 
318 
316 
313. 
3" 

11.40605 
40285 
39967 
39651 
39338 

8.  594=8 

59749 
60068 
60384 
60698 

321 
3'9 
316 

3H 
3" 

11.40572 
40251 

39932 
39616 

39302 

10.  00033 
00034 
00034 
00035 
'00036 

9.  99967 
99966 
99966 
99965 
99964 

45 
44 
43 
42 

41 

20 
21 
22 

=3 

=4 

II  4!  20 
41  12 

41  4 
40  56 
40  48 

o  18  40 
J8  48 
18  56 
19  4 

19  12 

8.  60973 
61282 
61589 
6.1894 
62196 

3°9 
307 
3=5 
302 
301 

11.39027 
38718 

334" 
38106 
37804 

8.  61009 
61319 
61626 
61931 

62234 

310 
307 
303 
3°3 
301 

11.38991 
78681 

28374 

-,8069 
37766 

10.00036 
00037 
00037 
00038 
00038 

9.  99964 

99963 
99963 
99962 
99962 

40 

? 

11 

-5 

CO 

?37 

29 

ii  40  40 
40  32 
40  24 
40  16 
40  8 

0  19  £0 
IJ  23 

19  3s 
19  44 
19-52 

8.  62497 
62705 
63091 
63385 
63678 

298 
296 
294 

293 
290 

"•375°3 
37205 
36909 
36615 
36322 

8.62535 
62834 

*3'3I 
63426 

63718 

299 
237 
295 
292 
291 

11.37465 
37166 
36869 

36574 

.36=82 

10.  00039 
00039 
00040 
00040 
00041 

9-  9996i 
99961 
99960 
99960 
99959 

35 
34 
33 
32 
3i 

30 
31 
32 
33 

34 

n  40  o 

39  52 
39  44 
33  36 
39  28 

O  20   0 
20  8 

20  16 

20  24 

20  32 

8.  63968 

64256 

64543 
64827 
65110 

288 
287 
284 
283 
281 

21.36032 

35744 
35457 
35  '73 
34890 

8.  64009 
64298 

64585 
64870 

fcS'St 

2Sg 
287 
285 
284 
281 

1  1-  3599' 
35702 

35415 
35130 
34846 

10.  00041 
00042 
00042 

00043 

00044 

9-  99959 
99958 
99958 

99957 
99956- 

3° 
29 
28 

27 
26 

35 
3° 

% 
X* 

39 

;i  39  20 
39  12 
39  4 
38  56 
3848 

o  20  40 

20  4" 
20  56 
21   4 
21  12 

8.  65391 
65670 

65947 
66223 

66497 

279 
277 
276 
274 
272 

11.34609 
3433° 
34053 
33777 
335°3 

8.  65435 
65715 
65993 
66269 

66543 

280 
278 
276 
274 
273 

"•34565 
34285 
34007 
3373' 
33457 

10.  00044 
00045 
00045 
00046 
00046 

9.  99956 
99955 
99955 
99954 
99954 

25 
24 
23 

22 
21 

40 

4' 
42 

43 
44 

ii  38  40 
38  32 
38  24 
38  1  5 
38  8 

O  21  2O 
21  28 
21  S6 
21  44 

21  52 

8.  66769 
67039 
67308 

67575 
67841 

270 
269 
267 
266 
263 

"•33231 
32961 
32692 
32425 
32159 

8.66816 
67087 

6SIS6 
67624 

67890 

2r 
269 

268 
266 
264 

11.33184 

32913 
32644 
32376 
32110 

10.  00047 
00048 
00048 

00049 

00049 

9-  90953 
99952 
99952 
99951 
99951 

2O 
19 

18 

17 
16 

4I 
46 

47 
48 

49 

ii  38  o 

37  52 
37  44 
37  36 
37  28 

0  22   0 
22   8 
22  l6 
22  24 
22  32 

8.68104 
68367 
68627 
68886 
69144 

263 
260 
259 
258 
256 

11.31896 
31633 
3'373 
'  3"'4 
30856 

8.68154 
68417 
68673 
68938 
69196 

263 
261 
260 
258 
257 

11.31846 
31583 
31322 
31062 
30804 

lo.  00050 
00051 
00051 
00052 
00052 

9-  9995s 
99949 
99949 
99948 
09948 

IS 
14 
13 

12 
II 

50 
5' 
52 
53 
54 

n  37  23 
37  12 

3l  i 
&  56 
36  48 

O  22  40 

22  48 
22  56 

23  4 

23  12 

8.  69400 
69654 
69907 

70I59 
70409 

254 
253 
252 
250 
249 

ii.  30600 
30346 

30093 
29841 
29591 

8.  69453 
69708 
69962 
70214 
70465 

255 
254 
252 
251 
249 

n.  3°547 

30292 
30038 
29786 
29535 

10.  00053 
00054 
00054 
00055 

00056 

9.  99947 
99946 
99946 
99945 
99944 

10 

o. 
8 

6 

!i 

!i 

g 

n  36  40 
36  32 

36  24 

36  16 
36  8 
36  o 

0  23  20 
23  28 
23  36 

23  44 
23  52 
24  o 

8.  70658 
70905 
71151 

71395 
71638 

71880 

247 
246 
244 

243 
242 
240 

11.29342 
29095 
28849 
28605 
28362 
28120 

8.  70714 
70962 
71208 

71453 
71697 
71940 

248 
246 

245 

244 
243 
241 

n.  29286 
29038 
28792 

28547 
28303 
28060 

10.  00056 
00057 
00058 
00058 
00059 
00060 

9.  99944 
99943" 
99942 
99942 
99941 
99940 

5 
4 
3 

2 
I 
O 

M. 

Hour  p.  M. 

Hour  A.  u. 

Cosine. 

Diff.  i'. 

Secant. 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant. 

Sine. 

M. 

92°                                                             81° 

180 


SINES,  TANGENTS,  AND  SECANTS. 
3°                                                                                                                                                           110° 

11. 

Hour  A.  H. 

Hour  P.M. 

Sine. 

Diff.  i'. 

Cosecant. 

Tangent. 

Did.  i'. 

Cotangent. 

Secan'. 

Cosine. 

M. 

o 

i 

2 

3 

4 

II   36     0 

35  52 
35  44 
35  36 
35  =8 

o  24     o 
24     8 
24  16 
24  24 

24  ••  ! 

8.  71880 
721:0 
72359 
72S97 
7^34 

240 
239 
23« 

237 
235 

II.  281:0 
27SSO 
27641 

2/403 
27166 

8.  71940 

72l8l 
72420 
7:659 
7:896 

241 
2-39 
239 
237 

236 

1  1.  28060 
27819 

27580 

27341 

27104 

IO.  00060 
00060 
00061 
00062 
00062 

9-  90940 
99940 
90939 
9993s 
99938 

60 
59 

5« 
57 
56 

I 

8 
9 

11  35  20 
35  «2 
35    4 
34  56 
34  48 

o  24  4  > 

24  48 
24  56 

25     4 
25    12 

8.  73069 

733°3 
73535 

73  T"  7 
73997 

234 
232 
232 
230 

229 

11.26931 
26697 
26465 
26233 
26003 

8-  73  '32 
733°6 
73600 

73832 
74063 

234 
234 
232 

23" 
2:9 

1  1  .  26868 
26634 
26400 
26168 
25937 

10.  00063 
00064 
00064 
00065 
00066 

9-  99937 
99936 

99936 
99935 
99934 

55 
54 
53 
52 
SJ 

10 

ii 

12 
13 

'4 

II  34  40 
34  32 
34  24 
34  16 
34    8 

o  25  20 

25    2S 

25  36 
25  44 
25  52 

8.  74226 

74454 
74680 
74906 
75  '30 

228 
226 
226 
224 
223 

11.25774 
25546 
25320 
25094 
24870 

8.  74:92 
745  •=! 
74748 
74974 
75'99 

229 
227 
226 
225 

224 

II.  25708 

25479 
25252 
250:6 
2480! 

10.  00066 
00067 
00068 
00068 

00069 

9-  99934 
99933 
99932 
99932 
9993' 

5° 
49 
48 

47 
46 

'5 
16 

\l 

iq 

ii  34    o 

33  52 
33  44 
33  36 
33  28 

o  26    o 
26    8 
26  16 
26  44 

26  32 

8-  75353 

75575 
75795 
76015 

76234 

222 
220 
22O 
219 
217 

II.  24647 
24425 
24205 

23985 
23766 

8-  75423 

75645 
75867 

76087 
76306 

222 
222 
22O 
219 

2IQ 

11.24577 
24355 
24133 

239  '3 
23694 

10.  00070 
00071 
00071 
00072 

00073 

9-  9993° 
999:9 
99929 
999:8 
909:7 

45 
44 
43 
42 
4' 

20 
21 

22 

23 

24 

ii  33  20 

33  '2 
33    4 

32  56 
32  48 

o  26  40 
26  48 
26  56 
S7    4 

27    12 

8.  76451 
76667 
76883 
77°97 
77310 

216 
216 

214 
213 

212 

11.23549 

23333 
23H7 
22903 

22690 

8.  76525 
76742 
76958 
77'73 
773S7 

217 

216 

215 
214 
213 

11.23475 

23258 
23042 
22827 
2:613 

10.  00074 

00074 
00075 

00076 

00077 

9-  999^6 
99926 
99925 
99924 
99923 

40 
39 
38 
37 
36 

25 
26 

27 
28 
29 

ii  32  40 

32  32 
32  24 
32  16 
32    8 

o  27  20 

27   28 
27   36 

27  44 
27  52 

8.  77522 
77733 
77943 
78152 
78360 

211 
210 

209 
208 

208 

11.22478 
22267 
22057 
2lS4S 
21640 

8.  77600 
77811 
78022 
78232 
78441 

211 
211 
2IO 
209 

20S 

ii.  22400 
22189 
21978 
21768 

21559 

10.  00077 
00078 

00079 

oooSo 
00080 

9.  999:3 
99922 
99921 
999:0 
999:0 

35 
34 
33 
32 
3J 

3° 
3< 
32 
33 

34 

ii  32     o 
3'  52 
3«  44 

3'  36 
31  28 

o  28     o 
28    8 
28  16 
28  24 
28  32 

8.  78568 

78774 
78979 
79i83 
79386 

206 
205 
204 
203 
202 

11.21432 
21226 
2I02I 
20817 
20614 

8.  78649 
78855 
79061 
79266 
7947° 

206 
206 
205 
204 
203 

ii.  21351 
21145 
20939 
20734 
20530 

10.  00081 
00082 
00083 
00083 
00084 

9.99919 
99918 

99917 
99917 
99916 

3° 
29 

28 

27 
26 

P 

i? 

39 

ii  31  20 

31    12 

31      i 

30   56 

30   48 

o  28  40 
28  48 
28  56 
29    4 

29    12 

8.  79588 
797S9 
79990 
80189 
80388 

201 
201 
199 
199 

'97 

II.  20412 
202  1  1 
200  1  0 
igSlI 
19612 

8.  79673 

79875 
80076 

80277 
80476 

202 
2O  I 
201 
199 

igS 

11.20327 
20125 
19924 

19723 
19524 

10.  00085 

00086 

1)0087 
00087 
oooSS 

9.99915 
99914 

99913 
999"3 
99912 

25 
24 
23 

22 
21 

40 
4' 
42 
43 
44 

II    30   40 

3°  32 
3°  24 
30  16 
30    8 

o  29  20 

29  28 
29  36 

29  44 
29  52 

8.  80585 
80782 
80978 

8n73 
81367 

197 
196 

«95 
194 

193 

II.  I94K 
I92IS 
19022 
18827 
18633 

8.  80674 
80872 
81068 
81264 
81459 

108 
196 
196 

'95 
194 

ii.  193:6 
19128 
18932 
18736 

18541 

10.  00089 
00090 
00091 
00091 
00092 

9.99911 
99910 
99909 
99909 
99908 

:o 

19 
18 

17 

16 

45 
46 

47 
48 

49 

ii  30    o 
29  52 
29  44 
29  36 
29  28 

o  30    o 
30     8 
30  16 

3°  24 
30  32 

8.81560 
81752 
81944 
82134 
82324 

192 
192 
190 
190 
189 

II.  18440 
18248 
18056 
17866 
17676 

8.  81653 
81846 
82038 
82230 

824:0 

193 
192 
192 
190 
190 

11.18347 
18154 
17962 
17770 
I758o 

10.  00093 
00094 

00095 

00096 
00096 

9-  999°7 
99906 
99905 
99904 
99904 

15 
'4 

«3 

12 
II 

5° 
51 
52 
53 

54 

n  29  20 

29    12 

28  56 
28  48 

o  30  40 

3°  48 
30  56 

31     4 

31    12 

8.82513 
82701 
82888 

83075 
83261 

188 
187 
187 
1  86 
185 

11.17487 
17299 
I7II2 
16925 
16730 

8.  82610 

82799 
82987 

83'75 
83361 

189 
188 
iS8 
1  86 
1  86 

ii.  17390 
17201 

«70'3 
16825 
16639 

10.  00097 
00098 
00099 

OOIOO 
OOIOI 

9-  99903 
99902 
99901 
99900 
99899 

10 

6 

55 
56 

ii 
£ 

II  28  40 
28  32 
28  24 

28  16 
28     8 
28    o 

o  31  20 

31  28 

3'  36 
3«  44 
31  S* 
32    o 

8.  83446 
83630 
83817 
83996 
84177 
8435» 

184 
183 

'!3 

iSi 

181 

181 

II.l6554 
16370 
16187 
I6OO4 
15823 
15642 

8-  83547 

83732 
83916 
84100 
84282 
84464 

^S 
184 

184 
182 
i£a 
182 

II.  16453 
16268 
16084 
15900 
I57I8 
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IO.  OOI02 
OOIO2 
OOIO3 
OOIO4 
OOIO? 
OOIOO 

9-  99898 
99898 
99897 
99896 
99895 
99894 

5 
4 
3 

2 
I 
0 

M. 

Hour  p,  M. 

Hour  A.M. 

Coa'.rc, 

Diff,  i'. 

Secant. 

Cotangent. 

Diff.  i' 

Tangent. 

Cosecant. 

Sine. 

M. 

93°                                                                                                                                                    86° 

SINES,  TANGENTS,  AND  SECANTS. 
4°                                       .                 175° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Dlff.  i'. 

Cosecant. 

Tangent. 

Dlff.  i'. 

Cotangent. 

Secant 

Cosine. 

M. 

0 

I 

2 

3 

4 

II  28  0 

27  52 
27  44 
27  36 
27  28 

O  32  o 

32  8 
32  16 
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32  32 

8.  84358 

84539 
84718 
84897 
85°75 

181 
179 
179 

I78 
177 

II.  15642 
15461 
15282 

'5'°3 
14925 

8.  84464 
84646 
84826 
85006 
85185 

182 
1  80 

i  So 
179 
178 

"•15536 

'5354 
'5'  74 
14994 
14815 

IO.  00106 
00107 
ooioS 
00109 
00109 

9.  99894 

99893 
99892 
99891 
99891 

60 

59 
58 

11 

8 
9 

II  27  20 
27  12 
27   A 

26  56 
26  48 

o  32  40 
32  48 
32  56 
33  4 
33  12 

8.  85252 

85429 
85605 
85780 
85955 

177 
I76 

175 
175 
173 

II.  14748 
I457I 
'4395 
14220 
14045 

8.  85363 
85540 
85717 
85% 
86069 

177 

'77 
176 
176 
'74 

11.  14637 
14460 
14283 
14107 
I393I 

10.  oo  no 

OOIII 
001  12 

00113 
00114 

9.  99890 
99889 
99888 
99887 
99886 

55 
54 
53 
52 
5' 

10 
II 

12 
13 
14 

II  26  40 
26  32 
26  24 

26  l6 

26  8 

o  33  20 
33  28 
33  36 
33  44 
33  S2 

8.86128 
86301 
86474 
86645 
86816 

173 
173 
171 
171 
171 

II.  13872 

13699 
'3526 

'3355 
13184 

8.  86243 
86417 
86591 
86763 
86935 

'74 
'74 
172 
172 
171 

"•'3757 

'3583 
'3409 
'3237 
13065 

10.  00115 

001  ID 
OOII7 
OOIlS 
OOII9 

9.  99885 
99884 
99883 
99882 
99881 

5o 
49 
48 
47 
46. 

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17 

18 
19 

II  26   O 

25  52 
25  44 

25  36 

25  28 

34  o 
34  8 
34  '6 
34  24 
34  32 

8.  86987 
87156 

87325 
87494 
87661 

169 
169 

i6J> 
167 

168 

ii.  13013 

12844 
12675 
12506 
12339 

8.  87106 
87277 
87447 
87616 
87785 

171 

170 
169 
169 
1  68 

ii.  12894 
12723 

12553 
12384 

12215 

10.  00120 
OOI2I 
OOI2I 
OOI22 
OOI23 

9.  99880 
99879 

99879 
99878 
99877 

45 
44 
43 
42 

4' 

20 
21 
22 

23 
24 

ii  25  20 

25  12 

25  2 

24  56 
24  48 

o  34  40 
34  43 
34  56 
35  4 
35  '2 

8.  87829 

87995 
88161 
88326 
88490 

166 
166 

165 
164 

164 

n.  12171 

12005 
11839 
11674 
11510 

8-  87953 
88120 
88287 

88453 
88618 

167 
167 
166 
'65 
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ii.  12047 
1  1  880 

"7'3 
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11382 

10.  00124 

00125 
OOI26 
00127 
OOI28 

9-  99876 

99875 
99874 

99873 
99872 

4° 

3?, 
38 

3l 
36 

25 
26 

27 
28 
29 

ii  24  40 

24  32 
24  24 
24  16 
24  8 

o  35  20 
35  28 
35  36 
35  44 

35  52 

8.  88654 
88817 
88980 
89142 
89304 

'<3 
'63 

162 
162 

1  60 

ii.  11346 
11183 
1  1  020 
10858 
10696 

8.  88783 
88948 
89111 
89274 
89437 

165 
'63 
'63 
'63 
161 

ii.  11217 
11052 
10889 
10726 
10563 

10.  00129 

00130 
00131 
OCH32 
00133 

9.  99871 
99870 
99869 
99868 
99867 

35 
34 
33 
32 
3' 

3° 
3i 
32 
33 

34 

ii  24  o 
23  S2 
23  44 
23  S6 
23  28 

o  36  o 
36  8 
36  16 
36  24 
3°  32 

8.  89464 
89625 
89784 

89943 
90102 

161 
159 
'59 
'59 
158 

ii.  10536 

l°375 
10216 
10057 
09898 

8.  89598 
89760 
89920 
90080 
90240 

162 
1  60 
1  60 
1  60 
'59 

ii.  10402 
10240 
10080 
09920 
09760 

10.  00134 
00135 
00136 

00137 

00138 

9.  99866 
99865 
99864 
99863 

99862 

3° 
29 
28 

2l 
26 

3! 
36 

37 
38 
39 

II  23  20 
23  12 

23  4 

22  56 
22  48 

o  36  40 
36  48 
36  56 
37  4 
37  '2 

8.  90260 
90417 

90574 
90730 
90885 

'57 

I5I 
156 

'55 

155 

II.  09740 

09583 
09426 
09270 
09115 

8.  90399 

90557 
90715 
90872 
91029 

158 
158 
'57 
'57 
'56 

ii.  09601 

09443 
09285 
09128 
08971 

10.  00139 

00140 
00141 
00142 
00  '43 

9.  99861 
99860 
99859 
99858 
99857 

25 
24 
23 

22 
21 

40 

41 
42 

43 
44 

II  22  40 

22  32 
22  24 

22  ID 
22   8 

o  37  20 
37  28 
37  36 
37  44 
37  52 

8.  91040 
91195 

91349 
91502 

91655 

'55 
'54 
'53 
'53 
152 

II.  08960 
08805 

0865! 
08498 
08345 

8.91185 
9  '340 

9'495 
91650 
91803 

'55 

'55 
'55 
'53 
'54 

11.08815 
08660 
08505 
08350 
08197 

10.  00144 
00145 
00146 
00147 
00148 

9-  99856 

99855 
99854 

99853 
99852 

20 

'9 
18 

17 
16 

45 

46 

47 
48 

49 

II  22   O 
21  52 

21  44 

21  36 
21  28 

o  38  o 
38  8 
38  16 
3»  24 
38  32 

S.  91807 

9'959 
92110 
92261 
92411 

152 
'5' 
'5' 
150 

150 

II.  08193 
08041 
07890 

°7739 
07589 

8.  91957 
92110 

92262 
92414 

92565 

'53 

'52 

152 
'5' 
'Si 

ii.  08043 
07890 

07738 
07586 

07435 

10.  00149' 
00150 
00152 

00153 

00154 

9.99851 
99850 
99848 

99847 
99846 

IS 
H 
13 

12 
II 

5° 
5' 

52 
53 

54 

II  21  20 
21  12 

21   4 
20  56 
20  48 

o  38  40 
38  48 
38  56 
39  4 
39  12 

8.  92561 
92710 
92859 
93007 
93154 

'49 
'49 
148 

'47 

147 

11.07439 

07200 
07141 
06903 
06846 

8.92716 
92866 
93016 
93165 
93313 

150 
150 

'49 
148 
149 

n.  0.7284 

07134 
06984 
06035 
06687 

10.  00155 
00156 

00157 

00158 
00159 

9-  99845 
99844 

99843 
99842 

99841 

10 
I 

55 
56 

ii 

59 
60 

II  2O  40 
20  32 

2O  24 
20  10 
20   8 

20  o 

o  39  20 
39  28 
39  36 
39  44 
39  52 
40  o 

8.  93301 
93448 
93594 
9374° 
93885 
94030 

Hl 
146 

146 
'45 
'45 
»44 

li.  06699 
06552 
06406 
06260 
06115 
05970 

8.  93462 
93609 
93  756 
93903 
94049 

94195 

'47 
'47 
147 
146 
146 
'45 

11.06538 
06391 
06244 
06097 

05951 
05805 

10.  00160 
00161 
00162 
00163 
00164 
00166 

9-  99840 

99839 
99838 

99837 
99836 

99834 

5 
4 
3 

2 
I 
O 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Difi.  i'. 

Secant 

Cotangent. 

Diff.  i'. 

Tangent. 

Cosecant. 

Sine. 

M. 

94°                                                              85° 

18. 


SINES,  TANGENTS,  AND  SECANTS. 
5°                                                              174° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

I 

2 

3 
4 

II  20  OO 
1952 
"9  44 
'936 
19  28 

0.40  o 
40  8 
40  16 
40  24 
40  32 

8.  94030 
94'  74 
943  '7 
94461 
94603 

o 

2 

4 
7 
9 

11.05970 
05826 
05683 
05539 
05397 

8.  94195 
94340 
94485 
94630 

94773 

O 

2 
4 
7 
9 

II.  05805 
05660 

°55'5 
053/0 
05227 

10.  00166 
00167 
00168 
00169 
00170 

o 

0 

o 
o 
o 

9-  99834 
99833 
99832 
99831 

99830 

60 

59 

58 

57 
56 

8 
9 

II  19  20 
19  12 

19  4 

18  56 

18  48 

o  40  40 
40  48 
40  56 
41  4 
4!  12 

8.  94746 
94887 
95029 
95170 
953'° 

ii 

'3 

15 

•20 

11.05254 

05»3 
04971 
04830 
04690 

8.  94917 
95060 
95202 

95344 
95486 

ii 
"3 

18 

20 

n.  05083 
04940 
04798 
04656 
04514 

10.  00171 
00172 

00173 
00175 

00176 

o 
o 
o 
o 
o 

9.  09829 
99828 
99827 
99825 
99824 

55 
54 
53 

52 
5' 

10 

ii 

12 

'3 
14 

II  1  8  40 
18  32 
18  24 
iS  16 
18  8 

O  41  20 
41  28 

41  36 
41  44 
41  52 

8.  95450 

95589 
95728 
95867 
96005 

22 

24 
26 
29 

3' 

n.  04550 
04411 
04272 
°4«33 
03995 

8.95627 

95767 
95908 
90047 
96187 

22 
24 
27 
29 

31 

11.04373 

04233 
04092 

03953 
03813 

10.  00177 
00178 
00179 
00180 
00181 

o 
o 
o 
o 
o 

9-  99823 
99822 
99821 
99820 
99819 

So 
49 
48 

47 
46 

15 
10 

17 

18 

19 

ii  18  o 
1752 
'744 
1736 
17  28 

o  42  o 
42  8 
42  16 
42  24 
42  32 

8.  96143 
96280 
96417 

96553 
96689 

33 
35 
37 
39 

42 

11.03857 
03720 
03583 
03447 
03311 

8.  96325 
96464 
96602 

96739 
96877 

33 
35 
38 
40 

42 

11.03675 
03536 
03398 
03261 

03123 

10.  00183 
00184 
00185 
00186 
00187 

o 

0 

o 
o 
o 

9.99817 
99816 
99815 
99814 
99813 

45 
44 

43 
42 

41 

20 
21 

22 

23 

24 

II  I  7  20 

1712 

17  4 

16  56 
16  48 

o  42  40 
42  48 
42  56 
43  4 
43  I2 

8.  96825 
96960 

97°95 
97229 
97363 

44 
46 

48 
5° 
53 

11.03175 
03040 
02905 
02771 
02637 

8.97013 
97150 
97285 
97421 
97556 

44 
46 

49 
5' 
53 

n.  02987 
02850 
02715 
02579 
02444 

10.  00188 
00190 
00191 
00192 

00193 

o 
o 
o 

0 

o 

9.  99812 
99810 
99809 
99808 
99807 

40 
39 
3* 
37 
3& 

25 
26 

27 

28 

29 

ii  16  40 
16  32 
16  24 
16  16 
16  8 

o  43  20 
43  28 
43  36 
43  44 
43  52 

8.  97496 
97629 
97762 
97894 
98026 

55 
57 
59 
61 

64 

ii.  02504 
02371 
02238 
02106 
01974 

8.  97691 
97825 

97959 
98092 
98225 

ii 

60 

62 
64 

ii.  02399 
02175 
02041 
01908 
01775 

10.  00194 
00196 
00197 
00198 
00199 

9.  99806 
99804 
99803 
99802 
99801 

35 
34 
33 
32 
3' 

3° 
3' 
32 
33 

34 

II  16  o 
1552 
>544 
1536 
15  28 

o  44  o 
44  » 
44  «6 
44  24 

44  32 

8.98157 
98288 
98419 

98549 
98679 

66 
68 
70 
72 
75 

ii.  01843 
01712 
01581 
01451 
01321 

8.  98358 
98490 
98622 

98753 
98884 

6t> 
69 
71 
73 
75 

ii.  61642 
01510 
01378 
01247. 
on  16 

IO.  O0200 
OO2O2 
OO2O3 
00204 
00205 

9.  99800 
99798 

99797 
99796 

99795 

3° 
29 
28 
27 
26 

3 

9 

39 

II  15  20 
15  12 

'S  4 

14  56 
1448 

o  44  40 
44  48 
44  56 
45  4 
45  '2 

8.  98808 

9S937 
99066 
99194 
99322 

77 
79 
81 
83 
86 

11.01192 
01063 
00934 
00806 
00678 

8.99015 
99145 
99275 
994°5 
99534 

77 
80 
82 
84 
86 

n.  00985 
00855 
00725 
00595 
004.66 

lo.  00207 

OO2o8 
O0209 
O02IO 
O02I2 

9-  99793 
99792 

99791 
99790 
99788 

25 
24 
23 

22 
21 

40 
4" 

42 

43, 
44 

11  14  40 

1432 
14  24 

14  16 
14  8 

o  45  20 
45  28 
45  36 
45  44 
45  52 

8.  9945° 
99577 
99704 

99830 
99956 

88 
90 
92 

94 
96 

ii.  00550 
00423 
00296 
00170 
00044 

8.  99662 
99791 
99919 
9.  00046 
00174 

89 
91 
93 
95 
97 

11.00338 
00209 
00081 
10.  99954 
99826 

10.00213 
O02I4 
00215 
O02I7 
00218 

) 

9-  99787 
99786 

99785 
99783 
99782 

20 
19 

18 

'7 

16 

45 
46 

47 
48 

49 

ii  14  o 
1352 
'344 
1336 
13  28 

o  46  o 
46  8 
46  16 
46  24 
46  32 

9.  00082 
00207 
00332 
00456 
00581 

99 

101 

«°3 
105 
107 

16.  99918 

99793 
99668 

99544 
99419 

9.  00301 
00427 

00553 
00679 
00801; 

IOO 
102 
104 
1  06 

108 

10.  99699 

99573 
99447 
99321 
99'95 

10.  00219 

O0220 
OO222 
OO223 
OO224 

9-  9978i 
99780 
99778 

99777 
99776 

'5 
14 
'3 

12 
II 

5° 
5' 
52 
53 
54 

II  13  20 
13  12 

13  1 
12  56 

12  48 

o  46  40 
46  48 
46  56 
47  4 
47  12 

9.  00704 
00828 
-0095J. 
01074 
01196 

no 

112 
114 

116 
118 

10.  99296 
99172 
99049 
98926 
98804 

9-  00930 
01055 
01  1  79 

01303 
01427 

111 
"3 
"5 
"7 

120 

10.  99070 
98945 
98821 
98697 

98573 

10.  00225 

CO227 
00228 
OO229 
OO23I 

9-  99775 
99773 
99772 

99771 
99769 

10 

6 

55 
5° 

11 
8 

II  12  40 
12  32 
12  24 
12  l6 
12  8 
12  0 

o  47  20 
47  28 
47  36 
47  44 
47  52 
48  o 

9.  01318 
01440 
01561 
01682 
01803 
01923 

121 

123 
125 
127 
129 
'32 

10.  98682 
98560 
98439 
98318 
98197 
98077 

9.01550 
01673 
01796 
01918 
02040 
02162 

122 
124 
126 
128 
»3' 
133 

10.  98450 

98327 

98204 
98082 
97960 

97838 

10.  00232 

00233 
00235 
00230 
00237 
00239 

99768 
99767 
99765 
99764 

99763 
99761 

5 
4 
3 

2 
I 

• 

It. 

Hour  i".  a. 

Hour  A.  M. 

Cosine. 

D1S. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

&MR6. 

M. 

95°                                                           84° 

f                                   SINES,  TANGENTS,  AND  SECANTS. 
C° 

..    m° 

M. 

Hour  A.  M. 

Hour  P.M. 

Sine. 

Diff. 

Cosecant. 

Tangent 

Diff. 

Cotangent. 

Secant, 

Diff. 

Cosine. 

M. 

o 
I 

2 

3 

4. 

II   12     O 

II   52 
1144 
II  36 
II  28 

O  48     0 

48    8 
48  16 
48  24 
48  32 

9-  01923 
02043 
02163 
02283 
02402 

O 
2 

0 

7 

10.  98077 
97957 
97«37 
97717 
97598 

9.02162 
02283 
02404 
02525 

02645 

O 
2 

4 
6 
8 

10.  97838 

97717 
97596 
97475 
97355 

10.  00239 

00240 
0024! 
00243 
00244 

O 
O 

o 
o 

o 

9-  9976i 

99760 

99759 
99757 
99756 

60 
59 
58 

11 

I 
9 

II    I  I  2O 
II   12 

ii    4 
10  56 
10  48 

0  48  40 

48  48 
48  56 
49    4 
49  12 

9.  02520 
02639 
0275.7 
02874 
02992 

Q 
11 

»3 

'5 
17 

10.  97480 
97361 
97243 
97126 
97008 

9.  os."66 
02885 
03005 
03124 
03242 

9 
ii 

'3 
IS 
«7 

13.  97234 
97"5 
96995 
96876 
96758 

10,  00245 

00247 

00248 
00249 
00251 

o 

0 

o 
o 
o 

9-99755 
99753 
99752 

99751 
99749 

55 
54 
53 
52 
5« 

10 
II 

12 

'3 

14 

II    10  40 

10  32 
10  24 
10  16 
10    8 

o  49  20 
49  28 
49  36 
49  44 
49  52 

9.  03109 
03226 
03342 
03458 
03574 

19 
20 

22 

24 
26 

10.  96891 

96774 
96658 
96542 
96426 

9-  9336i 
03479 
03597 
03^14 
03832 

19 

21 
23 

24 
26 

10.  96639 
96521 

96403 
96286 
96168 

10.00252 

00253 
00255 

00256 
00258 

o 
o 
o 

0 
0 

9-  99748 
99747 
99745 
99744 
99742 

So 
49 
48 

47 
46 

11 

17 

18 
«9 

II    10     0 

9  52 
944 
936 
9  28 

o  50    o 
50    8 
50'  1  6 
50  24 
50  32 

9.  03690 
03805 
03920 
04034 
04M9 

28 

3° 
3« 
33 
35 

10.96310 
96195 
96080 
95966 
95851 

9-  03948 
04065 
94181 
04297 
04413 

28 

3° 

32 

3t 
36 

10.  96052 

95935 
95819 

95703 

95-587 

10.  00259 
00260 
00262 
00263 
00264 

0 

o 
o 

0 

o 

9-  99741 
99740 

9973s 
99737 
99736 

45 
44 
43 
42 
4' 

20 

21 
22 
23 

24 

II      9  20 

9  12 

9    4 
856 
848 

o  50  40 
50-  48 
50  56 
5'    4 

51     12 

9.  04262 

04376 
04490 
04603 
04715 

37 
39 
Al 
43 

44 

10.95738 
95624 
95510 

95397 
95285 

9.  04528 
04643 
04758 
04873 
04987 

3» 

39 
4« 

43 
45 

10.  95472 
9535,7 
95242 
95127 

95°'3 

10.  00266 

00267 
00269 
00270 
00272 

0 

9-  99734 
99733 
9973' 
9973° 
99728 

40 
39 
38 

9 

II 

12 

29 

II    8  40 
832. 
8  24 
8  16 
8    8 

0   51    20 
51    28 

5"  36 
51  44 
5'  52 

9.  04828 
04940 
05052 
05164 
05275 

4b 
48 

5° 

52 

54 

10.95172 
95060 
94948 
94836 
94725 

9.05101 
'05214 

05328 
05441 
05553 

47 
49 
5« 
53 

54 

10.  94899 
94786 
94672 
94559 
94447 

10.  00373 

00274 

00276 

00277 

00279 

9.99727 
99726 

99724 
99723 
99721 

35 
34 
33 
32 
3i 

3° 
Si 
32 

33 

34 

II    8    o 

752 
744 
736 
728 

o  52    o 
52    8 
52  16 
52  24 
52  32 

9.  05386 

05497 
05607 
05717 
05827 

56 
57 

0? 

°3 

10.94614 
945°3 
94393 
94283 

94173 

9.  05666 
05778 
05890 
06002 
06113 

50 
58 
60 
62 
64 

IP.  94334 
94222 
94110 
9399s 
93887 

10.  00280 
00282 
00283 
00284 
00286 

9-  99720 
99718 

997'  7 
99716 

997M 

3° 

20 
28 

27 

26 

35 
36 
37 
38 

39 

ii    7  20 

712 

7   4 
656 
648 

o  52  40 

52  48 
52  56 

53    4 
53  '2 

9-05937 
06046 

°6'5S 
06264 
06372 

65 

67 
69 

70 
72 

10.  94063 
93954 
93845« 
93736 
93628 

9.  06224 
06335 
06445 
06556 
06666 

66 
68 
69 
7' 
73 

10.  93776 
93665 
93555 
93444 
93334 

10.  00287 
00289 
00290 
00292 

00293 

9-997I3 
99711 
99710 
99708 
99ro7 

25 
24 
23 

22 
21 

40 

41 
42 
43 

44 

ii    6  40 
632 
624 
6j6 
6    8 

o  53  20 
53  28 
53  36 
53  44 
53  52 

9.06481 
06589 
06696 
06804 
06911 

74 
76 

£ 
Si 

10.93519 
934" 
933°4 
93196 
93089 

9-  06775 
06885 
06994 
07103 
07211 

75 
77 
79 

Si 

83 

10.  93225 

93"5 
93006 
92897 
92789 

10.  00295 
00296 
00298 
00299 
00301 

9-  99705 
99704 
99702 
99701 
99699 

20 
19 

II 

45 
46 

47 
48 

49 

II    6    o 

552 
5  44 
536 
528 

o  54    o 
54    8 
54  16 
54  24 
54  32 

9.07018 
07124 
07231 

07337 

07442 

»3 
85 
87 
89 

9« 

10.  92982 
92876 
92769 
92663 
92558 

9-  07320 
07428 

°7536 
07643 
07751 

84 
86 
88 
90 
92 

10.  92680 

92572 
92404 

92357 
92249 

10.  00302 
00304 
00305 
00307 

00308 

9-  99698 
99696 

99695 
99693 
99692 

'5 
'4 
'3 

12 
II 

5° 
51 
52 
53 
54 

ii    5  20 
5  12 

5    4 

456 
448 

o  54  40 
54  48 
54  56 
55    4 
55  12 

9-  °7I)43 
0/653 
07758 
0786? 
07968 

93 
94 
96 

98 

100 

10.  92452 

92347 
92242 

92137 
92032 

9.  07858 
07964 
08071 
08177 
08283 

94 
96 
98 

99 

IOI 

10.92142 
92036 
91929 
91823 
91717 

10.00310 

00311 
00313 
00314 

00316 

9-  99690 
99689 
99687 
99686 
99684 

10 

6 

P. 
U 

59 
60 

ii    440 
432 
424 
416 

4    * 
4    6 

o  55  20 
55  28 
55  36 
55  44 
55  52 
56    o 

9.  08072 
08176 
08280 

08383 
08486 
08589 

102 

104 

106 
107 
109 
in 

10.  91928 
91824 

91720 
91617 
91514 
91411 

9.  08389 
08495 
08600 
08705 
08810 
08914 

'°3 
105 
107 
109 
in 
113 

10.91011 
91505 
91400 
91295 
91190 
91086 

10.00317 

00319 
00320 

OQ322 
00323 
00325 

9-  99683 
99681 
99680 
99678 
99677 
99675 

5 
4 
3 

2 

I 
0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

96°                                                                                                                                                           '88s 

SIXES,  TANGENTS,  AND  SECANTS. 
7°                                                                                                                                                       172° 

M. 

Hour  A.  M. 

Hour  r.  M. 

Sine. 

Did 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 
I 

2 

3 

4 

1140 
362 

3  44 
336 
3^2 

O  56     O 
56     8 
56  16 

56  24 
56  32 

9.  08589 
08692 
08795 
08897 
08909 

0 

: 
3 

6 

10.9141! 
91308 
91205 
91103 
9IOOI 

9.  08914 
09019 
09123 
09227 
09330 

O 
2 

3 

5 
7 

10.91086 
90981 
90877 

9°773 
00670 

10.  00325 

.00326 
00328 
00330 
00331 

O 

o 

o. 
a 

o 

9-  99675 
99674 
99672 
$9670 
99669 

60 
59 
58 
57 
5* 

6 

8 
9 

ii    3  20 
3  '2 

3    4 

256 

2  48 

o  56  40 
56  48 
56  56 
57     4 
J7  12 

9.09101 
09202 

09304 
09405 
09506 

8 
10 
ii 
13 
'4 

10.  00899 

90798 

90696 

90595 
90494 

9-  09434 
09537 
09640 
09742 
09845 

8 

10 

ii 
13 
15 

10.  90566 

90463 

90360 

90258 
90155 

10.  00333 

00334 
00336 

00337 
00339 

o 
o 
o 
o 
o 

9.99667 
99666 
99664 
99663 
99661 

55 
54 
53 
52 
5i 

10 

ii 

12 

13 

14 

II      2  40 
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97°                                                                                                                                                          82° 

185 


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Cosecant 

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M 

98°                                                              81° 

186 


SINES,  TANGENTS,  AND  SECANTS. 
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M. 

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Hour  p.  M. 

Sine. 

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Tangent. 

Diff 

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Cosine. 

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22977 
23°54 

45 
47 
48 

49 
50 

'°-  7/253 
77176 
77099 
77023 
76946 

10.  00610 
00612 
00615 
00617 
00619 

9-  9939° 
993S8 
993S5 
99383 
9938i 

25 

24 
23 

22 
21 

40 
4' 
42 
43 

44 

i  o  42  40 
4232 
42  24 
42  16 
42    8 

I    17  20 
17    28 
17   36 

17  44 
17  52 

9-  22509 
22583 
22657 
22731 
22805 

5° 
52 
53 

54 
55 

10.  77491 
774'7 
77343 
7/269 

77195 

9.23130 
23206 
23283 
23359 

23435 

52 

53 

ii 

57 

10.  76870 
/6794 
76717 
76641 

76565 

10.  00&2I 

00623 
00625 
00628 
00630 

2 

2 

9-  99379 
99377 
99375 
99372 
9937° 

20 

'9 
18 

17 
16 

45 
40 

47 
48 

49 

10  42    o 

4'  52 

41  44 

4'  36 
41  28 

I   18     o 
18     8 
18  16 
18  24 
18  32 

9.  2^878 
22952 
23025 
23098 
23171 

P 

59 
60 
62 

10.  77122 
77048 

76975 
76902 
76829 

9.23510 
23586 
23661 

23737 
23812 

58 
60 
61 
62 
63 

10.  76490 

76414 

76339 
76263 
76188 

10.  00632 

00634 

00636 
00638 
00641 

2 
2 

2 
2 
2 

9-  99368 
99366 

99364 
99362 

99359 

'5 
M 
'3 

12 
11 

5° 
5' 
52 

53 

54 

JO  41   20 
4!    12 
41     4 
40  56 
40  48 

18  40 
18  48 
18  56 
»9    4 

19    12 

9-  23244 
233"7 

23390 
23462 

23S3< 

63 
64 

65 
67 
68 

10.  76756 
76683 
76610 

76538 
76465 

9.  23887 
23962 

24037 
24112 
24186 

65 
66 

67 
69 

7o 

10.  76113 

76-038 
75963 
758.88 

75S'4 

10.  00643 

00645 

00647 
00649 
00652 

2 
2 
2 
2 
2 

99357 
99355 
99353 
9935' 
9934s 

10 

9 
8 

6 

55 
56 

H 
g 

10  40  40 

4°  32 
40  24 
40  16 
40    8 
40    o 

I    19    2O 
19    28 
19    36 

19  44 
IQ   52 
20      0 

9-  23607 
23679 
23752 
23823 

23895 
23967 

69 
7i 
72 
73 

74 
/6 

'o-  76393 

76321 
76248 
76177 
76105 
76033 

9.  24261 

24335 
24410 
24484 

24558 
24632 

7' 
73 

74 
75 
76 
7S 

'0-  75739 
75665 

75590 
755i6 
75442 
7536S 

10.  00654 
00656 

00658 

00660 
00663 
00665 

2 

2 
2 
2 
2 

2 

9-  99346 
99344 
99342 
99340 
99337 
99335 

5 

4 
3 

2 
I 
O 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent 

Cosecant. 

Diff. 

Sine. 

M. 

99°                                                                                                                                                                    80° 

187 


SINES,  TANGENTS,  AND  SECANTS. 
10°                                                                                                                                                  169° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff 

Cosecant. 

Tangent. 

Diff 

Cotangent. 

Secant. 

Diff 

Cosine. 

M. 

o 
I 

2 

3 

4 

IO  40    o 
3952 
3944 
3936 
3928 

I   2O     o 

20      8 
20    16 
20   24 

20   32 

9-  23967 
24039 
24110 
24181 
24253 

0 
I 

2 

3 

5 

10.  76033 
75961 
75890 
75819 

75747 

9.  24632 
24706 

24779 
24853 
24926 

0 
I 

2 

4 
5 

lo.  75368 

75294 
75221 

75147 
75°74 

IO.  00665 
00667 
00669 
00672 
00674 

O 
0 
O 
0 
O 

9-  99335 
99333 
99331 
99328 
99326 

60 

59 
58 
57 
56 

1 
9 

10  39  20 
39  12 
39    4 
3856 
3848 

I    20   40 
2O   48 
20    56 
21       4 
21    12 

24395 
24466 

24536 
24607 

6 

I 

9 

10 

10.  75676 

75534 
75464 
75393 

9.  25000 

25073 
25H6 

25219 

25292 

0 

7 
8 

9, 
ii 

10.  75000 

74927 
74854 
74781 
74708 

lo.  00676 
00678 
00681 
00683 
00685 

o 
a 

0 

o 

o 

9-  99324 
99322 

993  '9 
993'7 
99315 

35 

53 
£2 
<;i 

IO 

II 
12 
'3 
14 

10  38  40 
3832 
3824 
38  16 
38    8 

I    21    20 
21    28 
21    36 

21  44 

21    52 

9-  24677 
24748 
24818 
24888 
24958 

ii 

13 
14 

If 

ia.  75323 

75252 
75182 
75"2 

75042 

9.  25365 

25437 
25510 

25582 
25655 

12 
13 
14 
15 

16 

10.  74635 

74563 
74490 

74418 

74345 

10.  00687 
00690 
00692 

00694 
00696 

o 
o 
o 

9-993I3 
99310 
99308 
99306 
99304 

5° 
49 

47 

40 

15 
16 

17 
18 

19 

10  38    o 
3752 
3744 
3736 
3728 

I    22      0 
22      8 
22    16 
22    24 

22    32 

9.  25028 
25098 
25168 
25237 

;i 

19 

20 

22 

10.  74972 
74902 
74832 
74763 
74693 

9.25727 

25799 
25871 

25943 
26015 

18 

19 
20 

21 

22 

10.  74273 
74201 
74129 

74°57 
73985 

10.  00699 
00701 

00703 

00706 
00708 

9-  995°i 
99299 
99297 
99294 
99292 

45 
44 
43 
4^ 
4: 

30 
21 
22 
23 
24 

10  37  20 
37  12 
37   4 
3656 
3648 

I    22    40 
22    48 
22   56 

23     4 

23    12 

9-  25376 
25445 
25514 

25583 
25652 

24 

2 

27 

10  74624 

74555 
74486 

74417 

74348 

9.  26086 
26158 
26229 
26301 

26372 

24 

25 
26 

27 
28 

10.  75914 

73771 

73699 

73628 

10.00710 
00712 

00715 
00717 

00719 

9.  99290 
99288 
99285 
99283 
99281 

40 

P 

H 

25 
26 
27 
28 
29 

10  36  40 
3632 
36  24 
3616 
36    8 

I    23    20 
23    28 
23    36 

23  44 
23  52 

9.25721 
25790 
25858 
25927 
25995 

3° 
31 

32 

33 

10.  74279 
74210 
74142 

74073 
74005 

9-  26443 
26514 
26585 
26655 
26726 

29 
31 
32 

33 
34 

10.  73557 
73486 
734I5 
73345 
73274 

10.  00722 
00724 
00726 
00729 
00731 

9.99278 
99276 

99274 
99271 
99269 

35 
34 
33 
32 

3° 

32 
33 
34 

10  36    o 
35  52 
3544 
3536 
3528 

i  24    o 
24    8 
24  16 
24  24 

24  32 

9.  26063 
26131 
26199 
26267 

34 

? 
38 
39 

i°-  73937 
73869 
73801 

73733 
73665 

9-  26797 
26867 

26937 
27008 
27078 

35 
36 
38 
39 
40 

10.  73203 

73  "33 
73°63 
72992 
72922 

lo.  00733 

00736 
00738 

00740 

00743 

9-  99267 
99264 
99262 
99260 
99257 

30 
29 
28 

27 
26 

35 
36 
37 
38 
39 

10  35  20 
35  " 
35    4 
3456 
3448 

i  24  40 
24  48 
24  56 

25     4 

25    12 

9-  26403 
26470 
26538 
26605 
26672 

40 
41 
42 
43 

44 

10.  73597 
7353° 
73462 

73395 
73328 

9.  27148 
27218 

27288 

27357 

•    27427 

42 
44 

45 
46 

10.  72852 
72782 
72712 
72643 

72573 

10.  00745 

00748 
00750 
00752 
00755 

2 

9-  99255 
99252 
99250 
99248 
99245 

25 
24 
23 

22 
21 

40 

42 
43 
44 

10  34  40 
3432 
3424 
34  16 
34    8 

I    25    20 
25    28 
25    36 

25  44 
25  52 

9-  26739 
26806 
26873 
26940 
27007 

45 
47 
48 
<9 
5° 

10.  73261 
73194 
73127 
73060 

72993 

9-  2/496 
27566 
27635 
27704 
27773 

47 
48 

49 
Si 

52 

10.  72504 

72434 
72365 

72296 

72227 

10.00757 

00759 

00762 
00764 

00767 

2 
2 

2 
2 
2 

9-  99243 
99241 

99238 
99236 

99233 

2O 
19 

IS 

17 

16 

45 
46 

47 
48 
49 

10  34    o 
3352 
3344 
3336 
3328 

I    26      0 

26    8 
26  16 
26  24 
26  32 

9-  27073 
27140 
27206 
27273 
27339 

52 
53 

I 

10.  72927 

72860 
72794 
72727 

72661 

9.  27842 
27911 
27980 
28049 
28117 

53 
54 

11 

58 

IO.  72  1  "jo1 
72089 
72O2O 

7I%I 
71883 

10.00769 

00771 
00774 
00776 
00779 

2 
2 
2 
2 

2 

9.99231 
99229 
99226 
99224 
99221 

15 
14 

•3 

12 
II 

5° 
Si 

52 

53 
54 

10  33  20 
33  12 
33    4 
32  56 
3248 

i  26  40 
26  48 
26  56 
27    4 

27    12 

9.  27405 

27471 
27537 
27602 
27668 

59 
60 
61 

10.  72595 

72529 
72463 
72398 
72332 

9.28186 
28254 
28323 
28391 
28459 

00 

61 

62 
63 

16.  71814 

71746 
71677 

71609 

71541 

10.00781 
00783 
00786 

00788 

00791 

2 
2 
2 
2 

2 

9.99219 

99217 
99214 
99212 

99209 

30 

6 

U-»\O  t^-OO  O  O 
IO  U">  w»  in  IOVO 

10  32  40 

3232 
3224 
32  16 
32    8 
32    o 

I    27    2O 
27   28 
27   36 

27  44 

27  52 

28    o 

9-  27734 
27799 
27864 

27930 

2/995 
28060 

<>3 
64 

65 
66 

10.  72266 
72201 

72136 
72070 
72005 
71940 

9-  28527 

28595 

28662 
28730 
28798 
28865 

67 
68 
69 
71 

10.  7«473 
71405 

7:338 
71270 
71202 
7"3S 

10.  00793 
00796 
00798 
00800 
00803 
00805 

2 
2 
2 
2 
2 
2 

9-  99-20? 
99204 
99202 
99200 
99197 
99195 

5 
4 
3 

2 
I 
O 

M. 

Hour  t.  it. 

Hour  A.M. 

Cosine. 

Dint. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

100°                                                                                                                                                           79° 

Ibb 


SINES,  TANGENTS,  AND  SECANTS. 
11°                                                 '            16cS° 

M. 

Hour  A.  M. 

Hour  r  »i. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 
I 

2 

3 
4 

IO  32  0 
31  52 
31  44 

3'  36 

3128 

I  28  0 

28  8 
28  16 
28  24 
28  32 

9.  28060 
28125 
28190 
28254 
28319 

O 
I 

2 

3 
4 

10.  71940 

7'875 
71810 
71746 
71681 

9.  28865 

28933 
29000 
29067 
29134 

O 

I 
2 

3 

4 

10.71135 
71067 
71000 

70933 

70800 

IO.  00805 
00808 
008  1  o 
00813 
00815 

O 

0 

0 
O 
0 

9.99195 
99192 
99190 
99187 
99185 

Co 

59 
58 

H 

6 

I 
9 

10  31  20 

31  12 

31  t 

3056 
3048 

I  28  40 
28  48 
28  56 
29  4 

29  12 

9-  28384 
28448 
28512 
28577 
28641 

1 

I 

9 

10.  71616 

71552 

71488 
71423 

7«359 

9.  29201 
29268 

29335 
29402 
29468 

1 
8 
9 

10 

10.  70799 

70732 
70665 
70598 
70532 

10.00818 

OO22O 

00^23 

00825 

C0o28 

o 

0 

o 

0 

o 

9.99182* 
99180 
99177 
99175 
99172 

55 
54 
53 
52 
Si 

10 
ii 

12 
13 
H 

10  30  40 

3032 

3°  24 
30  16 

3°  8 

I  29  20 
29  28 

29  36 
29  44 

29  52 

9.  28705 
28769 
28833 
28896 
28960 

IO 

II 

12 

'3 

14 

10.  71295 
71231 
71167 
71104 
71040 

9-  29535 
29601 
29668 

29734 
29800 

II 

12 

'3 

«4 

15 

10.  70465 

70399 
70332 

70266 
70200 

io.  00830 
00833 
00035 

00838 

00840 

o 
o 

9.99170 
99167 
.   99165 
99162 
99160 

50 
49 
48 
47 
46 

«5 

16 

12 

19 

10  30  o 
29  52 
2944 
2936 
29  28 

i  30  o 
30  8 
30  16 
30  24 

3»  32 

9.  29024 
'  29087 
29150 
29214 
29277 

16 

i? 
18 

19 

20 

10.  70976 

70913 
70050 
70786 
70723 

9.  29866 
29932 
29998 
30064 
30130 

10 

11 
19 

20 

10.  70134 

70068 

70002 

69936 

69870 

lo.  00843 
00845 
00848 
00850 
00853 

9-99I57 
99155 
99152 

99150 
99147 

45 
44 
43 
42 
41 

20 

21 
22 

23 

24 

10  29  20 
29  12 

29  4 

28  56 
28  48 

i  30  40 
30  48 
30  56 
31  4 

jl  12 

9.  29340 

29403 
29466 
29529 
29591 

21 

22 
23 

24 

25 

10.  70660 

70597 
70534 
70471 
70409 

9.  30195 
30261 
30326 
30391 

30457 

22 
23 
24 

2! 

10.  69805 

69739 
69674 

69609 

69543 

io.  00855 
00858 

00860 

00863 
00865 

9.99145 
99142 
99140 

99137 
99135 

40 
39 
38 
37 
36 

25 
26 
27 
28 
29 

10  28  40 

2832 

28  24 
28  16 

28  8 

I  31  20 
31  28 

31  36 
3'  44 

3i  52 

9-  29654 
29716 

29779 
29841 
29903 

26 

27 
28 

29 
30 

10.  70346 
70284 
70221 
70159 
70097 

9-  30522 
30587 
30652 
30717 
30782 

27 
28 

29 
30 
31 

10.  69478 

69413 
69348 

69283 
69218 

io.  00868 
00870 
00873 
00876 
00878 

9.99132 

99130 
99127 
99124 
99122 

35 
34 
33 
32 
3i 

3° 

3' 
32 
33 

34 

10  28  0 

2752 
2744 
2736 

27  28 

I  32  o 
32  8 
32  16 
32  24 
32  32 

9.  29966 
30028 
30090 
30151 
3°2I3 

31 
32 

33 
34 
35 

10.  70034 

69972 

69910 

69849 
69787 

9.  30846 
30911 

3°975 
31040 
31104 

32 

33 
35 
36 
37 

10.  69154 
69089 
69025 
68960 
68896 

io.  ooSSi 

00883 
00886 
00888 
00891 

9.99119 
99117 
99114 
99112 
99109 

3° 
29 
28 

27 
26 

35 
36 
37 
3S 
39 

IO  27  20 
27  12 

27  4 

26  56 

26  48 

i  32  40 
32  48 
32  56 
33  4 
33  12 

9.30275 
30336 
30398 

3°459 
30521 

36 
37 
38 
39 
40 

10.  69725 
69664 
69602 

69541 
69479 

9.31168 
3'233 
3'297 
3'36i 
31425 

•38 
39 
40 

4i 
42 

10.68832 
68767 
68703 

68639 
68575 

io.  00894 
00896 
00899 
00901 
00904 

2 
2 

2 
2 
2 

9.  99106 
99104 
99101 
99099 
99096 

25 
24 

23 
22 
21 

40 

41 
42 

43 

44 

10  26  40 
26  32 
26  24 
26  16 
26  8 

i  33  20 
33  28 
33  36 
33  44 

33  52 

9-  3°582 
30643 
30704 
30765 
30826 

4> 

42 

43 

4£ 
46 

10.  69418 

69357 

69296 

69235 
69174 

9-  3M89 
31552 
31616 

31679 
3'743 

43 
44 
45 
46 
47 

10.  68511 

68448 
68384 
68321 
68257 

io.  00907 
00909 
00912 
00914 
00917 

2 
2 

2 
2 

2 

9-99093 
99091 
99088 
99086 
99083 

20 

:98 
17 

16 

4£ 
46 

47 
48 

49 

IO  26  O 
25  52 
2544 
2536 
25  28 

i  34  ° 
34  8 
34  16 
34  24 
34  S2 

o.  30887 

3°947 
31008 
31068 
31129 

47 
48 
49 
5° 

51 

10.69113 
69053 

68992 

68932 

68871 

9.  31806 
31870 

3'933 
31996 
3^59 

49 
5° 
51 

S2 

53 

10.  68194 
68130 
68067 
68004 

67941 

io.  00920 
00922 
00925 
00928 
00930 

• 

2 
2 
2 
2 

9.  99080 
99078 

99075 
99072 
99070 

•5 
«4 
13 

12 
II 

5° 
5' 
52 
53 

54 

to  25  20 

25  12 

25  4 

24  56 
2448 

i  34  40 
34  48 
34  56 
35  4 
35  '2 

9.31189 
31250 
3I3IO 
3'37° 
3M30 

52 
53 
54 
55 

56 

10.  68Sn 
68750 
68690 
68630 
68570 

9.32122 
32185 
32248 
323" 
32373 

54 
55 
56 

1 

10.  67878 

67815 

67752 
67689 
67627 

io.  00933 
00936 
00938 
00941 
00944 

2 

2 
2 
2 
2 

9-99067 
99064 
99062 
99059 
99056 

10 

9 
8 

6 

9 

57 
S3 

,59 
Go 

10  24  40 

2432 
2424 

24  16 
24  8 
24  o 

i  35  eo 
35  28 
35  36 
35  44 
35  52 
36  o 

9.  31490 

31549 
31609 
31669 
31728 
31788 

H 
59 
60 
61 
62 

10.  68510 
68451 
68391 

68331 
68272 
68212 

9-  32436 
32498 
32561 
32623 
32685 
32747 

59 
60 
61 

I3 
64 

65 

io.  67564 

67502 
67439 
67377 
67315 
67253 

io.  00946 

00949 
00952 

00954 

00957 

00960 

2 

2 
2 
2 
3 

3 

9-  99054 
99051 
99048 
99046 

99043 
99040 

5 
4 
3 

2 
I 
0 

M 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

-otangeiu. 

Diff 

Tangent. 

Cosecant. 

Diff. 

Sine. 

tf. 

101°                                                             78° 

189 


SINES,  TANGENTS,  AND  SECANTS. 
12°                                                     161° 

M. 

Hour  A.M. 

Hour  F.  M. 

Sine. 

Did 

Cosecant. 

Tangent. 

Diff 

Cotangent. 

Secant. 

Diff 

Cosine. 

M. 

O 

I 

2 

3 

4 

IO  24  O 
23  S2 
23  44 

23  36 

23  28 

1  36  0 
36  8 
36  Iff 
36  24 
36  J2 

9.31788 
3^47 
3'9°7 
31966 
32025 

0 

I 

2 

3 
4 

IO.  6^212 
68153 
68093 
68034 
67975 

9-  32-747 
32810 
32872 
32933 
32995 

0 
I 
2 
3 
4 

10.  67253 

67190 
67128 
67067 
67005 

10.  00960 
00962 
00965 
00968 
00970 

O 
O 

o 
o 
o 

9-  99040 
99038 

99035 
99032 
99030 

60 

59 
58 

y 

i 

I 

9 

10  23  20 
23  12 
23  4 

22  56 
22  48 

i  36  40 
36  48 
36  56 
37  4 
37  '2 

9-  32o84 

32143 

32202 
32261 
32319 

8 
9 

lo.  67916 

67857 
67798 
67739 

6760! 

9-  33°57 
33"9 
33180 
33242 

33303 

6 

9 

10.  66943 
66881 
66820 
66758 
66697 

10.  00973 
00976 
00978 
00981 
00984 

o 
o 
o 
o 
o 

9-  99027 
99024 
99022 
99019 
9.9016 

55' 
54 
53 
S2 
Si 

10 

11 

12 

'3 

14 

10  22  40 
22  32 
22  24 
22  l6 
22   8 

i  37  20 
37  28 
37  36 
37  44 
37  52 

9-  32378 
32437 
32495 
32553 
32612 

10 
10 

II 

12 

'3 

10.  67622 

67563 
67505 

67447 
67388 

9-  33365 
33426 

334S7 
33548 
33609 

10 

ii 

12 
13 
14 

•  10.  66635 

66574 
66513 

66452 
66391 

10.  00987 
00989 
00992 
00995 

00998 

o 

9-  990I3 
99011 
99008 
99005 
99002 

5° 
49 
48 

47 
46 

15 

16 

17 
18 

'9 

IO  22  O 
21  52 
21  44 
21  36 
21  28 

i  38  o 
38  8 
38  16 
38  24 
38  32 

9-  326/0 
32728 
32786 

32844 
32902 

H 

15 
16 

;87 

10.  67330 

67272 
67214 
67156 

67098 

9-  33670 
33731 
33792 
33853 
33913 

!i 

i? 

18 

19 

IO.  66330 

66269 
66208 
66147 

66087 

10.  OIOOO 

01003 
01006 
01009 

OIOII 

9.  99000 

98997 
98994 
98991 
98989 

45 
44 
43 
42 
41 

20 
21 
22 

23 

24 

IO  21  2O 
21  12 

21   4 
2O  56 
20  48 

i  38  40 
38  48 
38  56 
39  4 
39  '2 

9.  32960 
33018 

33°  75 
33133 
33i90 

19 
20 

21 

22 
23 

10.  67040 
66982 
66925 

66867 
66810 

9-  33974 
34034 
34°95 
34155 
34215 

20 

21 
22 

23 

24 

10.  66026 
65966 
65905 
65845 

65785 

lo.  01014 
01017 

OI020 
OIO22 
01025 

9.  98986 
98983 
98980 
98978 
98975 

40 

39 
38 
37 
36 

25 
26 

27 
28 
29 

I  o  20  40 

20  32 
2O  24 
26  l6 
20  8 

i  39  20 
39  28 
39  3° 
39  44 
39  52 

9-  33248 
333°5 
33362 
3342o 
33477 

24 
25 
2O 

27 
28 

10.  66752 

66695 
66638 
66580 
66523 

9-342/13 
34336 
34396 
34456 
345I6 

25 
26 

27 
28 

29 

lo.  65724 

65664 

65604 

65544 
65484 

10.01028 
OI03I 

OI°33 
01036 
01039 

9-  98972 
98969 

98967 
98964 
98961 

35 
34 
33 
S2 
V 

3° 
3' 
32 
33 
34 

IO  20  O 

1952 
1944 
1936 
1928 

I  40  o 
40  8 
40  16 
40  24 
40  32 

9-  33534 
33591 
33(H7 
33704 
3376i 

29 
29 

3° 
3i 
32 

IO.  66466 
66409 

66353 

66296 
4)6239 

9-34576 
34635 
34695 
34755 
34814 

3° 
3' 
S2 
33 

34 

10.  65424 

65365 
65305 
65245 
65186 

10.  01042 
01045 
01047 
01050 
01053 

2 

? 

9-  98958 
98955 
98953 
98950 
98947 

3° 
29 
28 

27 
26 

35 
36 
37 
38 
39 

10  19  20 
19  12 

19  4 
18  56 
18  48 

i  40  40 
40  48 
40  56 
41  4 

4!  12 

9-  33s  '  s 
33S74 
33931 
33987 

34°43 

33 

34 

H 

37 

10.  66  1  02 

66126 

66069 

60013 
65957 

9-  34S74 
34933 
34992 
35051 
35"i 

S 

$ 

39 

10.  65126 

65067 
65008 

64949 

64889 

10.  01056 
01059 
01062 
01064 

01067 

2 
2 
2 
2 
2 

9-  98944 
98941 
98938 
98936 

9S933 

25 
24 
23 

22 
21 

40 
4i 
42 
43 

44 

10  18  40 
1832 
18  24 
18  16 
18  8 

I  41  20 
41  28 

4'  36 
41  44 

41  S2 

9.  34100 
34156 
34212 
34268 
34324 

38 
39 
40 

41 
42 

10.  65900 
65844 

65788 

65732 
65676 

9-35I70 
35229 
35288 

35347 
354°5 

40 
41 
42 
43 
44 

lo.  64830 

64771 
64712 
64653 
64595 

10.  01070 

01073 

01076 
01079 
01081 

2 
2 

2 
2 

2 

9-  9893° 
9S927 
98924 
98921 
9S9I9 

20 
19 

18 

«7 
16 

45 
46 

47 
48 

49 

IO  18  O 

1752 
1744 

"7  36 
17  28 

i  42  o 
42  8 
42  16 
42  24 

42  32 

9-  3438o 
3443- 
34401 
34547 
34602 

43 

44 

45 
46 
47 

10.  63620 

65564 
65509 
65453 
65398 

9-  35464 
35523 
355Si 
35640 

35698 

4I 
46 

47 
48 

49 

10.  64536 

64477 
64419 

64360 

64302 

10.  01084 
01087 
01090 
01093 
01096 

2 

2 
2 
2 
2 

9.  98916 

98913 
98910 

98907 
98904 

IS 
'4 
13 

12 
II 

5° 
5' 
52 
53 
54 

10  17  20 
17  12 

I?  4 
1656 
16  48 

i  42  40 
42  48 
42  56 
43  4 
43  12 

9-  3465S 
34713 
34769 
34824 
34879 

48 
48 
49 
50 
51 

10.  65342 

65287 
65231 
65176 

65121 

9-35757 
35SI5 
35873 
3593' 
35989 

5° 
Si 
S2 
53 
54 

10.  64243 
64185 
64127 

64069 
64011 

10.  01099 

01  102 
OII04 
OII07 

oiuo 

2 
2 

2 
2 

3 

9.  98901 
98898 
98896 

98893 
98890 

10 
| 

55 
56 
57 
5S 
59 
60 

10  16  40 
16  32 
16  24 
16  16 
16  8 
16  o 

I  43  20 
43  28 
43  36 
43  44 
43  52 
44  ° 

9-  34934 
34989 
35°44 
35°99 
35154 
35209 

S2 
53 
54 
55- 
56 
57 

10.  65066 
65011 

64956 

64901 

64846 
64791 

9-  36047 
36105 
36163 
36221 
36279 
36336 

55 
56 
57 
58 

59 
60 

10-  63953 
63895 

t>3»37 
63779 
63721 
63664 

10.  01113 

OI5S6 

01119 

01  122 
OII25 
OII28 

3 
3 
3 
3 
3 
3 

9.  9SS8T 
98884 
oSSSi 
98878 

98875 
98872 

S 
4 
3 

2 
I 
O 

M. 

Hour  r.  M. 

Hour  A.  in. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

102°                                                          77° 

190 


SINES,  TANGENTS,   AND  SECANTS. 
13°                                                                                                                                                                   166° 

M. 

Hour  A  ». 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant: 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

I 
2 

3 
4 

JO  16     0 

IS  S2 
15  44 

»5  36 
15  28 

I  44     o 

44     8 

44  16 
44  24 
44  32 

9-  35209 
35261 

35318 
35373 

35427 

O 

I 

2 

3 

4 

10.  64791 

64737 
64682 
64627 
64573 

9-  36336 
36394 
36452 
365°9 
36566 

O 

I 
2 

3 

4 

10.  63664 

63606 
63548 
63491 
6.V134 

IO.  01  1  28 
01131 

°"33 
01136 
01139 

O 
o 
O 

o 
o 

9.  98872 
98869 
98867 
98864 
98861 

60 

59 
58 
57 

56 

I 

I 
9 

10  15  20 

15   12 

15  i 
1456 

1448 

I   44  40 
44  48 
44  56 
45     4 
45   >2 

9-  354»i 
35536 
3559° 
35644 
35^8 

4 

I 

lo.  64519 

64464 

64410 

64356 

64302 

9-  36624 
366Si 

36738 

36795 
36852 

i 

6 

87 

10.  63376 

6331  9 
63262 
63205 
63148 

lo.  01142 

01145 

01148 
oi  151 

01154 

o 
o 
o 
o 
o 

9.  9SS5S 

98855 
98852 
98849 

98846 

55 
54 
53 
52 
5i 

10 

II 

12 

'3 

14 

10  14  40 

1432 
14  24 

14  16 
14    8 

I  45  20 
45  28 
45  36 
45  44 
45  52 

9-35752 
35806 
35860 
359H 
35968 

9 

IO 

ii 
ii 

12 

ID.  64248 
64194 
64140 
64086 
64032 

9.  36909 
36966 

37023 
37080 

37137 

9 

IO 

ii 

12 
13 

10.  63091 

63034 
62977 
62920 
62863 

io.  01157 
01160 
01163 
01166 
oi  169 

9.  98843 

98840 

98837 
98834 
98831 

So 

41 
48 

4I 
£ 

11 
17 

18 
«9 

10  14    o 
>3  52 
'344 

13  3j> 
13  ^8 

I  46    o 
46     8 
46   16 
46  24 
46  32 

9.  36022 

36075 
36129 
36182 
36236 

'3 
H 
15 

16 
17 

10.  63978 

63925 
63871 
63818 
63764 

9-37I93 
37250 
373°6 
37363 
37419 

14 
15 

16 
II 

10.  62807 

62750 

62694 

62637 
62581 

io.  01172 

01175 

01178 
oi  181 
01184 

9.  98828 

98825 

98822 
98819 
98816 

45 
44 
43 

42 
41 

20 
21 
22 

23 
24 

10  13  20 

13   12 

13     I 

12   56 

12  48 

I  46  40 
46  48 
46  56 
47     4 
47  '2 

9.  36289 
36342 
36395 
36449 
36502 

18 
18 

19 

20 

21 

lo.  63711 

63658 

63605 

63551 
63498 

9-  37476 
37532 
37588 

37644 
37700 

19 
'9 

20 
21 

22 

10.  62524 

62468 
62412 

62356 

62300 

io.  01187 
01190 

01193 

01196 
01199 

9.98813 
98810 
98807 
08804 

98801 

40 

38 

37 
36 

% 

11 
29 

10   12  40 
12  32 
12  24 
12   l6 
12     8 

I  47  20 
47  28 
47  36 
47  44 
47  52 

9-  36555 
36608 
36660 

36713 
36766 

22 
23 
24 
25 
25 

10.  63445 
63392 
63340 
63287 
63234 

9-  37756 
37812 
37868 

37924 
37980 

23 
24 
25 
26 
2? 

10.  62244 

62188 
62132 

62076 

62020 

IO.  01202 
OI205 
OI208 
OI2II 
01214 

9-  98798 
98795 
98792 
98789 
98786 

35 
34 
33 
32 
3J 

30 

3' 
32 
33 

34 

IO  12     O 
"   52 

II  44 
II  36 
II  28 

I    48      0 

48     8 
48  16 
48  24 
48  32 

9-36819 
36871 
36924 
.36976 
37028 

26 
27 
28 
29 
30 

10.  63181 
63129 

6307,6 
63024 
62972 

9-  3So35 
38091 

38H7 
38202 

S8257 

28 
29 

3° 
31 

32 

10.  61965 
61909 

61853 

61798 
61743 

10.  01217 

OI22O 
OI223 
OI22§ 
OI229 

2 

2 

2 
2 

2 

9.  98783 
98780 
9S777 
98774 
9S771 

3° 
29 
28 

27 
26 

35 
36 
37 
3» 
59 

10  II   2O 
II    12 
II     4 
10  56 
10  48 

i  48  40 
48  48 
48  50 

49    4 
49  12 

9-  37°8i 
37133 
37i85 
37237 
37289 

3' 

32 
S2 

33 
34 

10.  62919 

62867 
62815 
62763 

62711 

9.383i3 
38368 
38423 
38479 
38534 

33 
33 
34 
35 
36 

10.  61687 
61632 
61577 

61521 
61466 

io.  01232 

OI235 
01238 
OI24I 
01244 

2 

2 
2 
2 
2 

9.  98768 

9s/65 
98-62 

98759 
98756 

25 

2* 
23 
22 
21 

40 
4i 
42 
43 
44 

10  10*40 
10  32 
10  24 
10  16 
10    8 

I  49  20 
49  28 
49  36 
49  44 
49  52 

9-  3734' 
37393 
37445 
374-37 
37549 

35 
36 

3 

39 

10.  62659 
62607 

62555 
62503 
62451 

9.  38589 
38644 
38699 

38754 
3SSo8 

% 

39 
40 

41 

10.  61411 

61356 
61301 
61246 
61  192 

io.  01247 

01250 
01254 
01257 
Olr6o 

2 

2 
2 
2 
2 

9-  98/53 
98750 
98746 

98743 
98740 

20 

19 
IS 

17 
16 

4£ 
46 

47 

48 

49 

IO   10      0 

9  52 
9  44 
9  36 

9  28 

I  50     o 
50     8 
50  16 
5°  24 

5°  32 

9-37600 
37652 
377=>3 
37755 
37806 

39 
40 

41 

42 

43 

10.  62400 

62348 
62297 
62245 

62194 

9-  38863 
38918 
38972 
39027 
39082 

42 
43 
44 
45 
45 

10.61137 
61082 
61028 
60973 
60918 

io.  01263 
01266 
01269 
01272 

01275 

2 

2 
2 
2 

2 

9-  98737 
98734 
98731 
98728 
98725 

15 
>4 
13 
12 
II 

5° 
51 
52 
53 

54 

10     9  20 

9  12 

9    4 
856 
848 

i  50  40 
50  48 
50  56 
51     4 

5I     12 

9-  3/3S8 
37909 
37960 
38011 
38062 

44 

4I 
46 

47 
47 

lo.  62142 
62091 
62040 
61989 
61938 

9-  39136 
39190 

39245 
39299 
39353 

46 

47 
48 

49 
5° 

lo.  60864 

60810 
60755 

60701 
60647 

IO.  OI2/S 

01281 
01285 

01  2S8 

01291 

3 
3 
3 
3 
3 

9.  98722 
98719 

98715 
98712 
98709 

IO 

6 

55 
56 
57 
58 

I9 
60 

to    8  40 
832 
824 
8  16 
8    8 
8    o 

I     51     20 
51     28 

5'  S6 
51   44 

5'   52 
52     o 

9-38113 
38j64 
38215 
38266 

38317 

38368 

48 
49 
5° 
Si 
52 
53 

10.  61887 

618^6 

61785 

61734 
61683 

61632 

9-  39407 
39461 
39515 
39569 
39623 

39677 

51 
52 
53 

54 
55 
56 

lo.  60593 

60539 

60485 

60431 

60377 
60323 

io.  01294 

01297 
01300 

01303 

0130(3 
01310 

3 
3 
3 
3 
3 
3 

9.  98706 

98703 
98700 

98697 
98694 
98690 

5 
4 
3 

2 

I 
O 

M. 

Hour  v.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

103°                                                                                                                                                                   76° 

191 


SINES,  TANGENTS,  AND  SECANTS. 
14°                                                                                                                      .                                    165° 

M. 

Hour  A.  M. 

Hour  f.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 
I 

2 

3 
4 

to    8    o 
752 
744 
736 
7  28 

I   52     0 
52    8 

52    ID 
52  24 
S2  32 

9.  38368 
38418 
38469 
3S5I9 
3857° 

O 
I 
2 

2 

3 

IO.  61632 
61582 

6l53« 
61481 

61430 

9-  39677 
3973' 
39/85 
39838 
39892 

O 
I 

2 

3 

3 

10.  60323 
60269 
60215 
60162 
60108 

10.01310 

0>3'3 
01316 
01319 
01322 

O 
O 
0 

o 
o 

9.  98690 
98687 
98684 
98681 
98678 

60 
59 

58 

57 
56 

i 

9 

10    7  20 
7  12 

7   4 
656 
648 

I   52  40 
S2  48 
52  56 
53    4 
53  12 

9.  38620 
38670 
38721 

3877I 
38821 

4 

I 

7 
7 

10.  61380 

61330 
61279 

61229 

61179 

9-  39945 
39999 
40052 
40106 
40159 

4 
I 

io.  60055 
60001 

59948 
59894 
59841 

10.01325 
01329 
01332 

OI335 
01  338 

o 
o 
o 
o 

0 

9.  98675 
9S67I 
98668 
98665 
98662 

55 
54 
53 
S2 
5' 

10 

it 

12 

'3 

14 

10    6  40 

632 
6  24 
616 
6    8 

i  53  20 
53  28 
53  36 
53  44 
53  52 

9-  3887i 
38921 

3S971 
39021 

39071 

8 
9 

10 

II 
II 

10.  61129 
61079 
61029 

60979 
6,0929 

9.  40212 
40266 
40319 
40372 
40425 

9 
10 

10 

II 

12 

io.  59788 

59734 
59681 
59628 
59575 

io.  01341 

OI344 
01348 

01351 

°'354 

9-  98659 
98656 
98652 
98649 
98646 

So 
49 

48 

47 
46 

15 

16 

\l 

"9 

10    6    o 

552 
5  44 

536 
528 

i  54    o 
54    8 
54  16 
54  24 
54  32 

9.39121 

39170 
39220 
39270 
39319 

12 

'3 

14 

«5 

15 

10.  60879 

60830 

60780 
60730 
60681 

9.  40478 

40531 
40584 
40636 
40689 

'3 

14 

\l 

17 

io.  59522 

59469 
59416 

59364 
593" 

10.01357 

01366 
01364 
01367 
01370 

9-  9S643 
98640 
98636 

98633 
98630 

45 
44 
43 
42 

41 

20 

21 
22 
23 
24 

10    5  20 
5  12 
5    4 

456 
448 

i  54  40 
54  48 
54  S6 
55    4 
55  '2 

9-  393°9 
394'8 
39467 
39517 
39;66 

16 

'7 

18 

19 

20 

10.  60631 
60582 

60533 
60483 

60434 

9.  40742 
40795' 
40847 
40900 
40952 

17 

18 

'9 
20 

21 

io.  59258 
59205 

59>53 
59100 

59048 

10.01373 

01377 
01380 

oi3?3 
01386 

9.  98627 
98623 
98620 
98617 
98614 

40 

11 
1 

26 

28 
20 

10    4  40 

432 
424 
4  16 
4    8 

i  55  20 
55  28 
55  36 
55  44 
55  52 

9.39615 
39664 

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53697 
53655 

9.  48080 
48126 
48171 
48217 
48262 

39 
39 
40 

4' 

42 

10.  51920 
51874 
51829 

5'783 
5  '738 

10.  01902 
01906 
01910 

01913 
01917 

3 
3 
3 
3 
3 

9.  98098 
98094 
98090 
98087 

98083 

10 
0 

55 
56 

15 
& 

9  44  40 
44  32 
44  24 
44  16 
44  8 
44  o 

2  IJ  20 
15  28 

'5  36 
IS  44 
15  S2 
16  o 

9-  46386 
46428 
46469 
46511 
46552 
46594 

39 
40 

4' 
4i 

42 

43 

10.  53614 

53572 

5353' 
53489 
53448 
53406 

9-  48307 
48353 
48398 

48443 
48489 

48534 

43 
43 
44 
45 
46 
46 

10.51693 
51647 
51602 

5'557 
51511 

51466 

10.  01921 

01925 

01929 

01933 
01937 

01940 

3 
3 

4 
4 
4 
4 

9-  98079 
98075 
98071 
98067 
98063 
98060 

5 
4 
3 

2 
I 
O 

M. 

Hour  p.  H. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

106°                                                             W° 

194 


SINES,  TANGENTS,  AND  SECANTS. 

\r 

62° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Co'.anRent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

1 

2 

3 

4 

9  44  0 
43  S2 
43  44 
43  36 
43  28 

2  16  0 
16  8 
16  16 
16  24 
16  32 

9-  46594 
46"35 
46676 
46717 
46758 

o 
I 
I 

2 

3 

10.  53406 
53365 
53324 
53283 
53242 

9-  48534 
4S579 
48624 
48669 
48714 

0 

I 
I 

2 

3 

io.  51466 
51421 
5!376 

5'331 
51286 

10.  01940 
01944 
01948 
01952 
01956 

0 
o 
o 
o 

0 

9.  98060 
98056 
98052 
98048 
98044 

60 
59 
5» 

57 
56 

I 

9 

9  43  20 
43  I2 
43  4 

42  56 

42  4» 

2  16  40 
16  48 
16  56 

>7  4 
17  12 

9.  46800 
46841 
46882 

46923 
46964 

3 
4 

5 

6 

10.  53200 
53"  59 
S3"8 
53°77 
53036 

9-  4S759 
48804 
48849 
48894 
48939 

4 

4 

7 

io.  51241 
5II96 
5H5' 
51106 
51061 

io.  01960 
01964 

01968 
01971 

01975 

0 
0 
0 

I 
I 

9.  98040 
98036 
98032 
98029 
98025 

55 
54 
53 
S2 

SJ 

10 

II 
12 

'3 
14 

9  42  40 
42  32 
42  24 
42  16 
42  8 

2  17  20 
17  28 

'7  36 

17  44 
>7  S2 

9.  47005 

47°45 
47086 
47127 
47168 

7 

I 

9 
9 

10.  52995 

52955 
52914 

52873 
52832 

9-  48984 
49029 

49073 
49118 

49163 

8 
9 

10 
10 

jo.  51016 

50971 
50927 
50882 
50837 

lo.  01979 

01983 
01987 

01991 

01995 

9.  9802  1 
98017 
98013 
98009 
98005 

50 

49 
48 
47 
46 

\S6 

17 
18 

19 

9  42  o 
41  52 
41  44 
4i  36 
41  28 

2  18   0 

li  8 
i$  16 
18  24 

18  32 

9-  47209 
47249 
4729° 
4733° 

4737" 

10 
ii 
li 

12 
"3 

10.  52791 

5275> 
52710 
52670 
52629 

9-  49207 
49252 
49296 
49341 

49385 

li 

12 
12 

«3 

14 

10.  50793 

50748 
50704 
50659 
50615 

io.  01999 
02003 
02007 

O2OII 

02014 

9.  98001 
97997 
97993 
97989 
97986 

45 
44 
43 
42 
41 

20 
21 
22 
23 
24 

9  41  20 

41  12 

41  4 

40  56 
40  48 

2  18  40 
18  48 
18  56 
19  4 

19  12 

9.47411 
47452 
47492 
47533 
47573 

'3 
14 

'5 

•5 
it 

10.  52589 

52548 
52508 

52467 

52427 

9-  4943° 
49474 
495  '9 
49563 
49607 

15 
15 
16 

"7 

18 

io.  50570 

50526 
50481 

50437 

50393 

IO.020I8 
O2022 
O2O26 
02030 
02034 

2 
2 

9.  97982 
979/8 
97974 
97970 
97966 

40 
39 
38 
37 
36 

25 
26 

27 
2S 

29 

9  40  40 
40  32 
40  24 
40  16 

40  8 

2  ig  20 
19  28 
19  36 

»9  44 
19  52 

9-476>3 
47654 
47694 

47734 
47774 

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>7 
18 

19 

19 

10.  52387 

52346 
52306 

52266 
52226 

9-  49652 
49696 
49740 
49784 
49828 

io 

19 
20 

21 
21 

io.  50348 

50304 

50260 
50216 

50172 

io.  02038 

O2O42 
02046 
O2050 
02054 

2 
2 

2 
2 
2 

9.  97902 
97958 
97954 
97950 
97946 

35 

34 
33 
32 
31 

3° 
3' 
32 

33 
34 

9  40  o 
39  S2 
39  44 
39  36 
39  28 

2  2O   O 
20   8 

20  16 
20  24 

20  32 

9.47814 
47854 
47894 
47934 
47974 

20 
21 
21 
22 
23 

IO.  r;2l86 
52146 
52106 
52066 
52026 

9-  49872 
49916 
49960 
50004 
50048 

22 
23 
24 
24 

25 

io.  50128 
50084 
50040 
49996 
49952 

10.  02058 
02062 
02066 
02070 

02074 

2 
2 
2 
2 
2 

9.  97942 
°7938 
97934 
9793° 
97926 

3° 

29 

28 

27 
26 

35 
36 
37 
5* 
30 

9  39  20 
39  12 
39  4 
38  56 
38  48 

2  2O  40 
20  48 
20  56 
21   4 
21  12 

9.  48014 
48054 
48094 
48i33 
48173 

23 
24 
25 
25 
26 

10.  51986 
5  "946 
51906 
51867 
51827 

9-  50092 
50136 
50180 
50223 
50267 

26 
26 
27 
28 

29 

Io.  49908 

49864 
49820 

49777 
49733 

io.  02078 
02082 
02086 

02090 
02094 

2 
2 
2 
3 

3 

9.  97922 
97918 

979H 
97910 
97906 

25 
24 
23 

22 
21 

4° 
41 
42 

43 

44 

9  38  40 
38  32 

38  24 

38  16 
38  8 

2  21  2O 
21  28 
21  36 

21  44 

21  S2 

9.48213 
48252 
48292 

48332 

48371 

27 
27 

28 

29 
29 

10.51787 
51748 
51708 
51668 
51629 

9.  '503  1  1 

5°355 
50398 
50442 

50485 

29 

3° 
3' 

32 
32 

io.  49689 
49645 
49602 
4955s 
49515 

io.  02098 

02102 
O2I06 
O2IIO 
02II4 

3 
3 
3 
3 

3 

9-  979°2 
97898 
97894 

9?S9° 
97886 

20 
'9 

IS 

17 

16 

45 
46 

47 
48 

41' 

9  38  o 
37  52 
37  44 
37  36 
37  28 

2  22   0 
22   8 
22  l6 
22  24 

22  32 

9.  4841  1 
48450 
48490 
48529 
48568 

3° 
31 
3' 
32 
33 

10.  51589 

5155° 
51510 

5i47i 
5H32 

9-  50529 
50572 
50616 

50659 
50703 

33 
34 
35 

% 

10.49471 
49428 
49384 
49341 

49297 

io.  02118 

02122 
O2I26 
02130 
02134 

3 
3 
3 
3 

3 

9.  97882 
97878 

97874 
97870 

97806 

IS 
H 
'3 

12 
II 

5° 
5' 

52 
53 

54 

9  37  20 
37  12 
37  4 

36  56 
36  48 

2  22  40 
22  48 
22  $6 

23   4 
23  12 

9.  48607 
48647 
48686 
48725 
48764 

33 
34 
35 

I 

io.  5  '393 
5'353 
5UI4 

5'275 
51236 

9.  50746 
507^9 
50833 
50876 
50919 

37 
37 
38 
39 

40 

io.  49254 

49211 
49167 
49124 

49081 

io.  02139 

02143 
02147 
02151 
02155 

3 
3 
3 

4 
4 

9.  97861 
97857 
97853 
9*849 

97845 

10 

7 
6 

55 
56 

2 

59 
60 

9  36  4° 
36  32 
36  24 
36  16 
36  8 
36  o 

2  23  2O 
23  28 
23  36 

23  44 
23  52 
24  o 

9.  48803 
48842 
48881 
48920 
48959 
48998 

37 
37 
38 
39 
39 
40 

10.51197 
51158 
51119 
51080 
51041 
51002 

9.  50962 
51005 
51048 
51092 

5H35 
51178 

40 

4« 

42 

43 
43 
44 

io.  49038 

48995 
48952 
48908 
48865 
48822 

io.  02159 
02163 
02167 
02171 

02175 
02179 

4 
4 
4 
4 
4 
4 

9.  97841 
97837 
97833 
97829 
97825 
97821 

5 
4 
3 

2 
I 
O 

M. 

Hour  p.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

107°                                                          22° 

195 


SINES,  TANGENTS,  AND  SECANTS. 
18°                                                              161° 

M. 

Hour*.  M, 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

I 

2 

3 
4 

9  36  0 

35  52 
35  44 
35  36 
35  28 

2  24  O 
24  8 
24  16 

24  24 
24  32 

9.  48998 

49037 
49076 

49"5 
49153 

0 
J 
I 
2 

3 

10.  51002 

50963 
50924 
50885 
50847 

9.51178 
5I22I 

51264 
51306 
5  '349 

O 

I 
I 

2 

3 

10.  48822 

48779 
48736 
48694 
48651 

10.  02179 
02183 
02188 
02192 
02196 

0 

o 

0 

o 
o 

9.97821 
97817 
97812 
97808 
97804 

60 

$ 
ll 

6 

8 
9 

9  35  20 
35  12 

35  i 
34  56 

34  48 

2  24  40 
24  48 
24  56 

25  4 

2$  12 

9.49192 

49231 
49269 
49308 
49347 

3 
4 
4 

6 

10.  50808 

50769 
50731 

50692 

50653 

9-5I392 

5  '435 
51478 
51520 
51563 

3 
4 
5 
6 
6 

10.  48608 

48565 
48522 
48480 
48437 

IO.  O220O 
02204 
02208 
02212 
O22I6 

o 

0 

o 

9.  97800 

97796 
97792 
97788 
97784 

55 
54 
53 
52 
51 

10 
ii 

12 

'3 

14 

9  34  40 
34  32 
34  24 
34  16 
34  8 

2  25  20 
25  28 
25  36 

25  44 
25  52 

9-  493S5 
49424 
49462 

4950° 
49539 

6 

8 
9 

lo.  506:5 

50576 
50538 

50500 

50461 

9.  51606 
51648 
51691 
51734 
51776 

8 

9 

10 

10.  48394 

48352 
48309 
48266 
48224 

10.  O222I 
02225 
02229 
02233 
02237 

9-97779 
97775 
97771 
97767 
97763 

5° 
49 
48 

47 
46 

15 

16 

17 
18 

'9 

9  34  o 
33  52 
33  44 
33  36 
33  28 

2  26   O 

26  8 

26  16 
26  24 
26,32 

9-49577 

496'5 
49654 
49692 
4973° 

9 
10 
ll 
ii 

12 

10.  50423 

50385 
50346 

50308 

50270 

9-  5l8i9 
51861 

5  '903 
51946 
51988 

10 

II 

12 
13 

'3 

10.  48181 

48139 
48097 

48054 

48012 

to.  02241 

02246 
02250 
02254 
02258 

9-  97759 
97754 
97750 
97746 

97742 

45 

44 

43 
42 

41 

20 
21 

22 

23 
24 

9  33  2° 
33  '2 
33  4 
32  56 
32  48 

2  26  40 
26  48 
26  56 

27  4 

27  12 

9.  49768 
49806 

49844 
49882 
49920 

'3 
'3 
'4 
H 
'5 

10.  50232 

50194 
50156 

50118 
50080 

9-  52031 
52073 
52H5 
52157 
52200 

'4 
>5 
'5 
16 

"7 

10.  47969 

47927 

47885 
47843 

47800 

10.  02262 
02266 
02271 

02275 
02279 

2 
2 
2 

9.97738 

97734 
97729 

97725 
97721 

40 

39 
38 
37 
36 

^ 
26 

27 
28 

29 

9  32  4° 
32  32 
32.24 
32-  16 
32  8 

2  27  20 
27  28 
27  36 

27  44 
27  52 

9-  4995s 
49996 

50034 
50072 
50110 

16 
16 
17 
18 
18 

10.  50042 
50004 
49966 

49928 

49890 

9.  52242 
52284 
52326 
52368 
52410 

'7 
18 

'9 
20 

20 

10.  47758 

47716 
47674 
47632 
47590 

10.  02283 

0228^7 
02292 
02296 
02300 

2 

2 
2 
2 
2 

9-977I7 
97713 
97708 

97704  ' 
977oo 

35 
34 
33 
32 
3i 

3° 
31 
32 
33 
34 

9  32  o 
3'  52 
3"  44 
3i  36 

31  28 

2  2S   0 

28  8 
28  16 
28  24 
28  32 

9.  50148 

5OI85 
50223 
50261 
50298 

19 
20 
20 

21 
21 

10.  49852 

49815 

49777 
49739 
49702 

9-  52452 
52494 
52536 
52578 
52620 

21 

22 
22 

23 

24 

10.  47548 

47506 
47464 
47422 
47380 

10.  02304 
02309 

02313 
02317 
02321 

2 

2 
2 

2 
2 

9-  97696 
97691 
97687 

9/683 
97679 

30 
29 
28 

27 
26 

35 
36 

38 
39 

9  3'  20 

3I  12 

3"  4 

3°  56 
3°  48 

2  28  40 
28  48 
28  56 

29  4 

29  12 

9-  50336 
50374 
50411 

50449 
50406 

22 

23 
23 
24 
25 

10.  49664 
49626 
49589 

49551 
495  H 

9.  52661 
52703 
52743 
52787 
52829 

24 

25 
26 

27 
27 

10-  47339 
47297 
47255 
47213 
47I7I 

10.  02326 

02330 

02334 
02338 

02343 

2 

3 
3 
3 
3 

9-  976/4 
9767° 
97666 
97662 
97657 

25 
24 
23 

22 
21 

4° 
4' 
42 
43 
44 

•9  3°  4° 
3°  32 
30  24 
30  16 
30  8 

2  29  20 
29  28 
29  36 

29  44 

29  52 

9-  50523 
50561 
50598 
50635 
50673 

25 
26 
26 
27 

28 

10.  49477 

49439 
49402 

49365 
49327 

9.  52870 
52912 
52953 
52995 
53037 

28 

29 
29 

3° 
31 

lo.  47130 
47088 

47047 
47005 

46963 

10.  02347 

02351 
02355 

02360 

02364 

3 
3 
3 
3 
3 

9-  97653 
97649 
97645 
97640 
97636 

20 
19 

18 

17 

16 

45 
46 

47 
48 

49 

9  30  o 
29  52 
29  44 
29  36 
29  28 

2  30   0 

30  8 
30  16 

3°  2"4 
30  32 

9.50710 
50747 
50784 
50821 
50858 

28 
29 

3° 
3° 
3' 

10.  49290 

49253 
49216 

49'79 
49142 

9-  53078 
53120 

53'6i 
53202 

53244 

3' 
32 
33 
34 
34 

10.  46922 
46880 
46839 
46798 
46756 

10.  02368 

02372 
02377 

02381 

02385 

3 
3 
3 
3 
3 

9-  97632 
97628 
97623 
97619 
97615 

IS 
14 
13 
12 
II 

5° 
51 

52 
53 

54 

9  29  20 
29  12 
29  4 
28  56 
28  48 

2  30  40 
3°  48 
3°  56 

3'  4 
31  12 

9.  50896 
50933 
5°97° 
51007 

5  '°43 

3i 
•32 
33 
33 
34 

10.49104 

49067 
49030. 
48993 
48957 

9-  53285 
53327 
53368 
534°9 
5345° 

3I 
36 

36 

37 
38 

10.  46715 

46673  , 

46632 

46591 
4655° 

10.  02390 

02394 
02398 

02403 
02407 

4 
4 
4 
4 
4 

9.  97610 
97606 
97602 
97597 
97593 

IO 

7 
6 

11 

57 
5^ 
59 
60 

9  28  40 
28  32 
28  24 
28  16 
28  8 
28  o 

2  31  20 
3I  28 

3'  36 
3"  44 
31  52 
32  o 

9.  51080 
51117 

5"54 
51191 
51227 
51264 

35 
35 
36 
37 

II 

10.  48020 

48883 

48846 
48809 

48773 
48736 

9-  53492 
53533 
53574 
536i5 
53656 
53697 

t 
39 

40 
41 
41 

42 

10.  46508 
46467 
46426 

46385 

46344 
46303 

10.  02411 
02416 
02420 

02424 

02429 

02433 

4 
4 
4 
4 
4 
4 

9-  97589 
97584. 
97580 

97576 
97571 
97567 

5 
4 
3 

2 
I 
O 

M. 

Houri'.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

108°                                                                 11° 

196 


SINKS,  TANGENTS,  AND  SECANTS. 
19° 

160° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tajigent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0. 

I 

2 

3 
4 

9  28  o 
27  S2 

27  42 
27  36 
27  28 

2  32  O 
32  S 
32  16 
32  24 
32  32 

9.51264 

5'3°> 
5«338 
5>374 
51411 

o 
I 
I 
2 
2 

10.  48736 
48699 
48662 

4»  26 

48589 

9-  53697 
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53779 
53820 
53S6i 

O 

I 
I 
a 

3 

IO.  46303 
46262 
46221 
46180 
46139 

«o.  02433 
02437 
02442 
02446 
02450 

o 

o 
o 
o 
o 

9-  97567 
97563 
9755s 
97554 

9755° 

60 
59 

5s 

I! 

9 

9  27  20 

27  12 

27  4 
26  56 
26  48 

2  32  40 
32  48 
32  56 

33  4 
33  >2 

9-  5  '447 
51484 
51520 
5'557 
5  '593 

3 
4 
4 

5 

5 

10.  48553 
48516 
48480 

48443 
48407 

9-  53502 
53943 
53984 
54025 
54065 

3 
4 
5 

10.  46098 

46057 

46016 

45975 
45935 

10.  02455 

02459 
02464 
02468 

02472 

o 
o 

9-  97545 
97541 
97536 
97532 
975-8 

55 

54 
53 
S2 
5' 

10 
ii 

12 

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14 

9  26  40 
26  32 
26  24 
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33  36 
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9.51629 

51666 
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5  '738 
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9.  54106 

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9 

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49 
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47 
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18 
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25  S^ 
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34  8 
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39 
38 
37 
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27 
28 
29 

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18 
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41 
42 
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25 
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34 
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39  36 
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34 
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35 
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10.  46769 

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9.55910 
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56067 
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10.  44090 

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10.  02678 

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4 
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M. 

109°                                                             70° 

197 


SINES,  TANGENTS,  AND  SECANTS. 
'23°                                                                                                                                                         159° 

M. 

HOUI1  A.  M. 

flour  p.  M. 

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59 
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9  19  20 

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3 
4 
4 

6 

10.  43697 
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10.02724 
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9.97276 
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54 
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50 

49 
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47 
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15 

16 

17 
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19 

9  18    o 
17  52 
17  44 
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10 
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12 
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10.  43307 
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43190 
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10.  02771 

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23 
24 
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• 

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M. 

110°                                                                                                                                                       69° 

SINES,  TANGENTS,  AND  SECANTS. 
21°                                                                 158° 

M. 

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Hour  p.  M. 

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28 

29 
29 

10.  39211 
39182 

39154 
39125 
39097 
39069 

9.  64688 
64722 
64756 
64790 
64824 
64858 

S2 
32 
33 
33 
34 
35 

IQ-353I2 
35278 

35244 
35210 

35176 
35142 

10.  03899 

03905 

03910 
03916 
03921 

03927 

5 
5 

5 
5 

Q.  96101 
96095 
96090 
96084 
96079 
96073 

5 
4 
3 

2 

: 
o 

M. 

Hour  t-.  M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

113°                                                                                                                                                          66° 

201 


SINES,  TANGENTS,  AND  SECANTS. 
2*°                                                             155° 

M. 

Hour  A.  M 

Hour  p.  M 

Sine. 

Diff 

Cosecant. 

Tangent. 

Diff 

Cotangent 

Secant 

Diff 

Cosine. 

M. 

O 

I 

2 

3 
4 

8  48  o 
47  52 
47  44 
47  S6 
47  28 

3  12  o 
12  8 

12  16 
12  24 
12  32 

9.  60931 
60960 
60988 
61016 
61045 

O 
o 
I 

I 

2 

10.  39069 
39040 
39012 
30984 
38955 

9.  648-8 
64892 
64926 
64960 
64994 

0 

I 
I 
2 
2 

10.35142 
35108 

35°74 
35040 
35006 

lo.  03927 

03933 
03938 
03944 
03950 

O 
0 

o 
o 
o 

9-  96073 
96067 
96062 
96056 
96050 

60 

9 

I 

8 
9 

8  47  20 
47  12 
47  4 
46  56 
46  48 

3  '2  4° 
12  48 
12  56 

'3   4 
13  12 

9-  6l°73 
61101 
61129 
61158 
61186 

2 

3 
3 
4 
4 

10.  38927 

38899 
38871 
38842 
38814 

9.  65028 
65062 
65096 
65130 
65164 

3 
3 

4 
4 

s 

10.  34972 
34938 
349°4 
34870 
34836 

10.  03955 
03961 
03966 
03972 
03978 

o 

( 

9.  96045 
96039 
06034 
96028 
96022 

55 
54 
53 
52 
Si 

10 
it 

22 
'3 

>4 

8  46  40 
46  32 
46  24 
46  16 
46  8 

3  J3  20 

13  28 
'3  36 

'3  44 
'3  52 

9.  61214 
61242 
61270 
61298 
61326 

5 

6 
6 

lo,  38786 

38753 

3873° 
38702 

38674 

9.65197 
65231 
65265 
65299 

65333 

6 
6 
7 

8 

lo.  34803 
34769 
34735 
347°i 
34667 

10.  03983 
03989 
°3995 
04000 
04006 

9.96017 
96011 
96005 
96000 
95994 

5° 
49 
48 

47 
46 

*s 

16 

'7 
18 

n 

8  46  o 
45  52 
45  44 
45  36 

45  28 

3  '4  o 
14  8 
14  16 

14  24 

'4  32 

9.61354 
61302 
61411 
61438 
61466 

7 

I 
8 
9 

10.  38646 
38618 

38589 
38562 

33534 

9-  65366 
65400 

65434 
65467 
65501 

8 
9 
9 

10 

ii 

10.  34634 
34600 
34566 
34533 
34499 

10.  04012 
04018 

04023 

04029 

04035 

I 

2 
2 
2 
2 

9-  95988 
95982 
95977 
9597' 
95965 

45 
44 
43 
42 
41 

CO 
21 
C2 

-3 
24 

8  45  20 
45  '2 
45  4 
44  56 
44  48 

3  '4  40 
14  48 
«4  56 
15  4 

15  12 

9-  6r494 
61522 
61550 
61578 
61606 

9 
10 
10 
II 
II 

10.  38506 
38478 
33450 
38422 
38394 

9-  65535 
65568 

65602 
65636 
65669 

ii 

12 
12 
13 

'3 

10.  34465 

34432 
34398 
34364 
3433« 

10.  04040 
04046 
04052 
04058 
04063 

2 
2 
2 
2 
2 

9-  959bo 
95954 
95948 
95942 
95937 

40 

3? 

38 

3£ 
3° 

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27 

23 

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8  44  40 
44  32 
44  24 
44  16 
44  8 

3  IS  20 

15  28 

15  36 
15  44 

15  52 

9.  61634 
61662 
61689 
61717 

61745 

12 
12 
12 

>3 

13 

10.  38366 

38338 
383" 
38283 

38255 

9.65703 

65736 
65770 
65803 
65837 

'4 

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15 

16 
16 

10.  34297 
34264 
34230 
34197 
34163 

lo.  04069 

04075 

04080 
04086 
04092 

2 
2 
3 
3 
3 

9-  95931 
95925 
959:0 

95914 

95908 

35 
34 

33 
32 
3r 

3° 
3Z 

32 
33 

34 

8  44  o 
43  52 
43  44 
43  36 
43  28 

3  16  o 
16  8 
16  16 

16  24 
16  y. 

9.61773 
61^00 
61828 
61856 
61883 

'4 
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15 

10.  38227 
38200 

38172 

38'44 
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9.  65870 
65904 
65937 
6597« 
66004 

>7 

11 

18 
'9 

10.34130 
34096 
34063 
34029 
33996 

10.  04098 

04103 

04109 

04115 

04121 

3 

3 
3 
3 
3 

9-  95902 

95897 
95891 

95885 
95879 

3° 
29 
28 

27 
26 

35 
S6 

M 
39 

8  43  20 
43  >2 
43  4 

42  56 
42  48 

3  16  40 
16  48 
16  58 
17  4 

17  12 

9.  61911 

6'939 
61966 
61994 
62021 

16 
'7 
17 
18 
18 

10.  38089 
38061 

38034 
38006 

37979 

9.  66038 
66071 
66104 
66138 
66171 

20  • 
20 

21 
21 

22 

10.  33962 

339=9 
33S96 
33862 
33829 

10.04127 

04132 
04138 
04144 

04150 

3 
3 
4 
4 

4 

MLl 
95862 
65856 
9585° 

25 

24 
23 

22 
21 

40 
41 
42 
43 
44 

8  42  40 
42  3Z 
42  24 
42  16 
42  8 

3  '7  " 
17  28 
17  36 
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9.  62049 
62076 
62104 
62131 
62159 

18 
J9 
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20 

Jo.  3  795  ' 
37924 
37896 
37869 
3784« 

9.  66204 
66238 
66271 
66304 
66337 

22 
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24 

25 

l°-  33796 
33.762 
33729 
33696 
3.3663 

10.  04156 
04161 
04167 

04173 
04179 

4 

4 
4 

4 
4 

9.  95844 
95839 

95833 
95827 
95821 

20 
19 

18 

'7 

16 

45 
46 

47 

48 

49 

8  42  o 
41  52 
41  44 

4'  36 

41  28 

3  i£  o 
18  8 
18  16 
18  24 

18  32 

9.  62186 
62214 
62241 
62268 
62296 

21 
21 
22 
22 
23 

10.37814 
37786 
37759 
37732 
377°4 

9.66371 
66404 

66437 
66470 
66503 

Zl 
26 

26 

27 

27 

10.  33629 

3359s 
33563 
33530 
33497 

10.  04185 
04190 
04196 

04202 
04208 

4 
4 

5 
5 
5 

9-958I5 
95810 
95804 
95798 
95792 

'5 
H 
'3 

12 
II 

5° 
5' 

52 
53 

54 

8  41  20 

41  12 

41  4 

40  36 
40  48 

3  18  40 
18  48 
18  56 
19  4 

19  12 

9-  62323 
62350 

62377 
62405 
62432 

23 

24 
24 
24 

25 

10.  37677 
3765a 
37623 
37595 
37568 

9.  66537 
66570 
66603 
08636 
66669 

28 
28 
29 
30 
30 

i°-  33463 
3343° 
33397 
33364 
33331 

10.  04214 
04220 

04225 
04231 
04237 

5 
5 
5 
5 
5 

9.95786 
9578o 
95775 
95769 
95763 

10 

7 
6 

55 
56 

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59 
60 

8  40  40 
40  32 
4°  24 
40  16 
40  8 
40  o 

3  19  2 

19  28 

»9  36 
19  44 
19  52 

20   0 

9.  62459 
62486 
62513 
62541 
62568 
62595 

26 
26 
27 
27 
28 

10.  37541 
37514 
37487 
37459 
37432 
37405 

9.  66702 

66735 
66768 
66801 
60834 
66867 

3i 
3i 
32 
32 
33 
33 

10.  33298 
33265 
33232 
33  '99 
33  '66 
33»33 

10.  04243 

04249 
04255 

04261 
04267 
04272 

5 
5 

0 

6 
6 

9-95757 
95751 
95745 
95739 
95733 
95728 

5 
4 
3 

2 

I 
0 

M. 

lour  p.  M. 

iour  A.  M. 

Cosine. 

DiS. 

Secant. 

otangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

114=                                                                 65° 

SINES,  TANGENTS,  AND  SECANTS. 
25°                                                                                                                                                          154° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Did 

Cosecant. 

Tangent. 

Diff 

Cotangent. 

Secant. 

Diff 

Cosine. 

M. 

O 

z 
z 

3 

4 

8  40     O 
39  52 
39  44 
39  36 
39  28 

3   20      O 
20      8 

20  16 
20  24 

20    32 

9-  62595 
62622 
62649 
62676 
62703 

O 
0 

I 
I 

2 

10-  374°5 
3737s 
3735' 
37324 
37297 

9.  66867 
66900 
66933 
66966 
66999 

0 
I 
I 
2 
2 

io.  33133 
33'00 
SSO6? 
33034 
33°oi 

io.  04272 
04278 
04284 
04290 
04296 

0 

o 
o 
o 

0 

9.957:S 
95722 
95716 
95710 
95704 

60 
59 
58 
57 
S6 

9 

8  39  20 
39  12 
39    4 
3856 
38  48 

3   20  40 
20    48 
2O    56 
21      4 
21     12 

9.62730 

62757 
62784 
62811 
62838 

2 

3 
3 

4 
4 

10.  37270 

37243 
37216 

37189 
37162 

9-  67032 

67065 
67098 

67'3' 
67163 

3 
3 
4 
4 
S 

10.  32968 

32935 
32902 
32869 
32837 

io.  04302 
04308 

043M 

04320 
04326 

9-  95698 
95692 
95686 
95680 
95674 

55 
54 
53 
52 
S' 

10 

II 

12 
13 
H 

8  38  40 
38  32 
38  24 
38  16 

38.  8 

3    21    20 
21    28 
21    36 

21  44 

21    52 

9.  62865 
62802 
62918 

62945 
62972 

4 
5 

1 
6 

10.37135 
37108 

37082 

37055 
37028 

9.  67196 
67229 
67262 
67295 
67127 

I 
7 

8 

io.  32804 

32771 
32738 
32705 
32673 

LO.  04332 
04337 
04343 
04349 
°4355 

9.  95668 
95663 
95657 
95651 
95645 

5° 
49 
48 

47 
46 

16 

"7 
18 

19 

8  38     o 
37  52 
37  44 
37  36 
37  28 

3    22      O 
22      8 
22    l6 
22    24 
22    32 

9-  62999 
63026 
63052 

63079 
63106 

7 

87 
8 
8 

10.  37001 

36974 
36948 

36921 
36894 

9.  67300 

67393 
67426 

67458 
67491 

8 
9 
9 

10 

10 

io.  32640 

32607 
32574 
32542 
32509 

io.  04361 

04367 
04373 
04379 
04385 

2 
2 
2 

2 
2 

9-  95639 
95633 
95627 
95621 
95615 

45 
44 
43 

42 

4i 

20 
21 
22 
23 

24 

8  37  20 
37  '2 

37    4 

36  56 

36  48 

3    22    40 
22    48 
22    56 

23      4 
23    12 

9-63133 
63  '59 
63186 

63213 
63239 

9 
9 
10 

10 

ii 

10.  36867 
36841 
36814 

36787 
36761 

9-  67524 
67556 
67589 
67622 
67654 

n 
ii 

12 
12 

«3 

io.  32476 

32444 
32411 

32378 
32346 

io.  04391 

04397 
04403 
04409 
04415 

2 
2 
2 
2 
2 

9-  95609 
95603 
05597 
95S9I 
95_S|jS 

40 
39 
38 
37 

36 

s 

12 

29 

8  36  40 

36  32 
36  24 
36  16 
36     8 

3  23  20 

23    28 
23    36 

23  44 
23  52 

g.  63266 
63292 
633'9 
6,^5 

633/2 

ii 
ii 

12 
12 

13 

i°-  36734 

36708 
36681 

36655 
36628 

9.  67687 
67719 
67752 
67785 
67817 

14 
14 
>5 

15 

io.  32313 

32281 
32248 

32215 
32183 

io.  04421 

04427 
04433 
04439 
04445 

3 

3 
3 
3 
3 

9-95579 
95573 
95567 
95561 

95555 

35 
34 
33 
32 
21 

3° 
3i 

32 
33 
34 

8  36    o 
35  52 
35  44 
35  36 
35  28 

3  24    o 
24    8 
24  16 
24  24 
24  32 

9-  63398 
63425 
63451 

63478 
63504 

«3 
14 
H 

i5 
'S 

10.  36602 

36575 
36549 
36522 
36496 

9.  67850 
67882 
67915 

67947 
67980 

16 
«7 
'7 
18 
18 

10.32150 
32118 

32085 
32053 

32020 

io.  04451 

04457 
04463 

04469 

04475 

3 
3 
3 
3 
3 

9-  95549 
95543 
95537 
95531 
95525 

30 
29 
28 

27 
26 

i 

38 

39 

8  35  20 
35  '2 
35    4 
34  56 
34  48 

3  24  4° 
24  48 
24  56 

25     4 

25    12 

9-63531 
63557 
63583 
63610 

63636 

!i 

16 

i? 
'7 

10.  36469 

36443 
36417 
36390 
36364 

9.  680  J'2 
68044 
68077 
68109 

68142 

19 

20 
20 
21 
21 

io.  31988 

31956 
35923 
31891 

31858 

io.  04481 

04487 
04493 

04500 
04506 

4 
4 
4 
4 
4 

9-955I9 
95513 
95507 
955oo 

95494 

25 
24 
23 

22 
21 

40 
4' 
42 
43 
44 

8  34  40 
34  32 
34  24 
34  '6 
34    8 

3  25  20 
25  28 

25  36 
25  44 
25  52 

9.  63662 
63689 

63715 
63741 
63767 

18 
18 
«9 
'9 
'9 

10.  36338 

363" 

36285 

36259 
36233 

9.  68174 
68206 
68239 
68271 
68303 

22 
22 
23 
23 
24 

io.  31826 

31794 
31761 

3'  729 
3i697 

io.  04512 
04518 

04524 

0453° 

04536 

4 

4 
4 
4 
4 

9-  95488 
95482 
95476 
95470 
95464 

2O 
19 

18 

'7 
16 

45 
46 

4Z 
48 

49 

8  34    o 
33  52 
33  44 
33  S6 
33  28 

3  26    o 
26     8 
26  16 
26  24 
26  32 

9-  63794 
63820 
63846 
63872 
63898 

20 
20 
21 
21 
22 

10.  36206 

36180 

36154 
36128 

36102 

9.  68336 
68368 

68400 
68432 
68465 

24 
25 

25 

26 

27 

io.  31664 

31632 

31600 

31568 
31535 

io.  04542 
04548 
04554 

04560 
04566 

5 
5 
5 

5 
5 

9-  9545s 
95452 
95446 
95440 
95434 

15 
14 

13 

12 
II 

5° 
51 

S2 
53 
54 

8  33  20 
33  12 
33     4 
32  50 

32  43 

3  26  40 
26  48 
26  56 
27    4 

27    12 

9-  63924 
63950 

63976 
64002 
64028 

22 

23 
23 
23 
24 

10.  36076 
36050 

36024 
35998 
35972 

9-  68497 
68529 
68561 

68593 
68626 

27 
28 
28 
29 
29 

10.31503 
31471 
31439 
31407 

3'374 

10.04573 
04579 
045  S5 
04591 

04597 

5 
5 
5 
5 

S 

9-  954=7 
95421 

95415 
95409 

95403 

IO 

9 
8 

7 
6 

55 
56 

P 

59 
60 

8  32  40 
32  32 
32  24 
32  16 
32    8 
32     o 

3  27  20 

27   28 
27    36 

27  44 
Z7  S2 
28    o 

9.  64054 
64080 
64106 
64132 
64158 
64184 

24 
25 
25 
26 
26 
26 

10.  35940 

35920 
3^894 

35868 

35842 
35816 

9.  CSojJ 
68690 
68722 

68754 
C37S5 
68818 

30 
3° 
3' 
3' 
32 
33 

10.31342 

3»3'9 
3.278 

31246 

31214 
31182 

i  o.  04603 
•  04609 
04616 

04622 
04628 
04634 

6 
6 
6 
6 
6 
6 

9-  95397 
95391 
95384 
9537s 
95372 
95366 

5 

4 
3 

2 

I 
O 

M. 

Hour  p.  M. 

Hour  A.  M.I    Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

115°                                                                                                                                                          64° 

SINES,  TANGENTS,  AND  SECANTS. 
26°                                                             153° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 
I 

2 

3 
4 

8  32  o 

3'  52 
3'  44 

3'  36 
31  28 

3  28  0 
28  8 
28  16 
28  24 
28  32 

9.  64184 
64210 
64236 
64262 
64288 

O 

O 

I 
I 

2 

10.35816 
35790 

35764 
35738 
35712 

9.  68818 
68850 
68882 
68914 

68916 

o 

I 
I 
2 
2 

Jo.  31.182 

31150 
31118 

31086 

31054 

IO.  04634 
04640 
04646 
04652 
04659 

O 
0 

o 

0 

o 

9-  95366 
9536° 
95354 
9534» 
9534' 

60 

59 
58 
57 
56 

6 

8 
9 

S  31  20 
31  u 

31  t 

3°  56 
30  48 

3  28  40 
28  48 
28  56 
29  4 

29  12 

9-643I3 
64339 
643b5 
64391 
64417 

2 

3 
3 

3 
4 

10.  35687 

35661 
35635 
35609 
35583 

9.  68978 
65010 
69042 
69074 
69106 

3 
3 
4 
4 
5 

10.  31022 

30990 

30958 
30926 
30894 

10.  04665 
04671 
04677 
04683 
04690 

9-95335 
95329 
95323 
953'  7 
953'o 

55 
54 
53 
S2 
5' 

10 

II 

12 

'3 
«4 

8  30  40 

3°  S2 
30  24 
30  16 
30  8 

3  29  20 

29  28 

29  36 
29  44 
29  52 

9.64442 
64468 

64494 
64519 

64545 

4 
5 
5 

6 

IO-35558 
35532 
35506 
354SI 

35455 

9-  6913* 
69170 
69202 

69234 
69266 

6 

7 
7 

lo.  30862 

3083° 
30798 
30766 

30734 

10.  04696 
04702 
04708 

04714 
04721 

9-  95304 
95298 
95292 
95286 
95279 

5° 

49 
48 

*1 

46 

'5 

10 

17 

18 

'9 

8  30  o 
29  52 
29  44 
29  36 
29  28 

3  3°  o 
30  8 
3°  '6 
30  24 
3°  32 

9.  64571 

64596 
64622 
64647 

64673 

6 
7 

8 
8 

to.  35429 

354°4 
35378 
35353 
35327 

9.  69298 
69329 
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69393 
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8 
8 
9 
9 

10 

10.  30702 

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2 
2 
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9-  95273 
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95254 
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45 
44 
43 

42 

41 

20 

21 
22 

23 
24 

8  29  20 

29  12 

29  4 

28  56 
28  ft 

3  3°  40 
30  48 
30  56 
3«  4 

31  12 

9.  64698 
64724 
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8 
9 
9 

10 
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10.  35302 
35276 

35251 
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9.69457 
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12 
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30480 

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10.  04758 

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2 
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3 

9-  95242 
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40 

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11 

25 
26 

27 
28 
29 

8  28  40 
28  32 
28  24 
28  16 
28  8 

3  3«  20 

31  28 

3'  36 
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9.  64826 
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64877 
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12 
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10.35174 
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9.95211 
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35 
34 
33 
32 
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33 

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8  28  o 
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26  56 
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33  4 
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16 

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10.34921 
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3  33  20 
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9.  65205 
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65255 
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17 
17 
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20 
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3  35  20 
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9.  65580 
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23 
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25 
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9.  OCO2O 

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4 
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M. 

Hour  p.  u. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

TanjCKt. 

Cosecant. 

Diff. 

Sine. 

M. 

116°                                                                63° 

204 


SINES,  TAXGEXTS,  AND 

27° 

SECANTS. 
152° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff 

Cotangent. 

Secant. 

Diflf 

Cosine. 

M. 

o 
i 

2 

3 
4 

8  34    o 

23   52 
23  44 

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36    8 
36  16 

36  24 
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i 

2 

10.  34295 
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o 
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2 
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10.  29283 

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10.  05012 
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2 
3 

3 
4 

10.34172 

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9.  70873 
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70935 

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3 
3 
4 
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10.  29127 

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10.  05044 
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55 
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52 
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10 
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6 
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10.  33925 
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9.  711-84 
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10.  28816 

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2 
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45 
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3  3s  4° 

38  48 

38  56 
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9.  66197 
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9 
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10.  33803 
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9-  71339 
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12 
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10.  28661 
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26 
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27 
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3  43  20 
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9.  67042 
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23 
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29 
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3° 
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5 
4 
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2 
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M. 

Hour?.  M. 

Hour  A.M. 

Cosine  . 

DiS. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

nr                                                                                                     62° 

205 


SINES,  TANGENTS,  AND  SECANTS. 
28°                                                             151° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

I 
z 
3 
4 

8  16  .0 
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15  44 
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15  28 

3  44  ° 
44  8 

44  16 
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9.  67161 
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c 
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2 

10.  32839 
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9.  72567 
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9-  94593 
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59 
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11 

8 
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8  15  20 

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15  4 

14  56 
14  48 

3  44  4° 
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3 
3 
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9.  72720 
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4 
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10.  27280 

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27189 
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55 
54 
53 
52 
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10 

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12 
13 
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M  32 
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3  45  20 
45  28 
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9.  67398 
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10.  32602 

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7 
7 

10.  27128 

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9.  94526 
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50 
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10.  32485 

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9-  73023 
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10.  26977 
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20 
21 
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23 
24 

8  13  20 

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13  4 

12  56 
12  48 

3  46  40 
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9 
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10.  32367 

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9-  73  '75 

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10 
ii 
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12 
12 

10.  26825 

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26735 

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39 
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10 
10 
10 

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10.  32250 

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14 
14 

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35 
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15 
16 
16 
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10.  26524 

26493 

26463 

26433 
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10.  05610 

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3 
4 
4 
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29 

28 

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3I 
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37 
38 
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10  56 
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10.  32018 
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18 
18 
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06693 

7 
7 
7 

7 
7 
7 

9-  93344 
93337 
933-9 
933P2 
933'4 
93307 

S 

4 

^ 

2 
I 
O 

M. 

Hour  P.M. 

Hour  A.M. 

Cosine. 

Diff. 

Secant. 

Cotangent 

Diff 

Tangent. 

Cosecant. 

Dig. 

Sins. 

II. 

120°                                                                                                                                                        59° 

20$ 


SINES,  TANGENTS,  AND  SECANTS. 

31°                                                     =   148° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

tt. 

o 
I 

2 

3 

4 

7  52  o 
51  52 
51  44 
5'  36 
51  28 

480 
8  8 
8  16 
8  24 
8  32 

9.71184 
71205 
71226 

71247 
71268 

o 

o 
I 

I 
I 

IO.  28816 
28795 
2S/74 

2^753 
28732 

9-  77S77 
77906 

77935 
7  J963 
77992 

o 
o 
I 
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2 

10.  22123 
22094 
22065 
22037 
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IO.  06693 
06701 
06709 
06716 
06724 

O 
0 

o 
o 
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9-  933°7 
93299 
93291 
93284 
93276 

60 
59 
58 
57 
56 

6 

8 
9 

7  51  20 

51  12 

51  4 

50  56 
50  48 

4  8  40 
8  48 
8  56 

9  4 

9  '2 

9-  71289 
71310 

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71352 
71373 

2 
2 

2 

3 
3 

10.  28711 
28690 

28669 
28648 
28627 

9.  7&02O 

78049 
78077 

78106 

78135 

2 

3 
3 
4 
4* 

10.  21980 

21951 
21923 
21894 
21865 

10.06731 

06739 
06747 
06754 
06762 

9.  93269 
93261 

93253 
93246 

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55 
54 
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52 

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10 

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12 

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14 

7  5°  4° 
5"  32 
5°  24 
50  16 
50  8 

4  9  20 
9  28 
9  36 
9  44 
9  52 

9-  71393 
714:4 

7M35 
71456 

7H77 

3 
4 
4 
4 
5 

10.28607 

28586 
28565 

28544 

28523 

9-  78163 
78192 
78220 
78249 
78277 

5 

6 
6 
7 

io.  21837 

21808 
21780 

21751 
21723 

io.  06770 
06777 
06785 

06793 
06800 

2 
2 

2 

9-  93^30 
93223 
932i5 
932°7 
93200 

5° 

49 
48 
47 
46 

15 

:6 

17 
18 

19 

7  50  o 
49  52 
49  44 
49,  36 
49  28 

4  10  o 
10  8 
10  16 
lo  24 
10  32 

p  71498 
71519 

71539 
71560 
71581 

5 

1 

6 

7 

10.  28502 

28481 
28461 

28440 

28419 

9.  78306 
78334 
78363 
78391 
78419 

7 
8 
8 
9 
9 

io.  21694 

21666 
21637 

21609 
21581 

10.  06808 
06816 
06823 
06831 
06839 

2 
2 
2 
2 

2 

9-  93192 
93i84 
93177 
93169 
93161 

45 
44 
43 
42 
41 

20 
21 
22 

23 
24 

7  49  20 
49  '2 
49  4 

48  56 
48  48 

4  10  40 
10  48 
10  56 
ii  4 

II  12 

9.  71602 
71622 

71643 
71664 
71685 

7 

8 
8 
8 

10.  28398 

28378 

28357 
28336 

28315 

9-  78448 
78476 
78505 
7^533 
78562 

9 

10 
IO 

ii 
ii 

io.  21552 

21524 
21495 
21467 
21438 

io.  06846 
06854 
06862 
06869 
06877 

3 
3 

3 
3 
3 

9-93IS4 
93145 
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93131 

93123 

40 
39 

1 

25 
26 

27 
28 
29 

7  48  40 
48  32 
48  24 
48  16 
48  8 

4  II  20 

II  28 
11  36 

ii  44 

n  52 

9.71705 
71726 

7  "747 
71767 
71788 

9 
9 
9 

10 
10 

io.  28295 

28274 
28253 
28233 

28212 

9-  78590 
76618 
78647 
78675 
78704 

12 
12 
13 
13 
M 

io.  21410 
21382 

2-1353 

213:5 

21296 

10.06885 
06892 
06900 
06908 
06916 

3 
3 
3 
4 

4 

9-93II5 
93108 
93100 
93092 
93084 

35 
34 
33 
32 
3t 

3° 
3' 

32 
33 

34 

7  48  o 
47'52 
47  44 
47  361 
47  28 

4  12   0 
12   8 
12  l6 
12  24' 
12  32 

9.  71809 
71829 
71850 

71870 

71891 

10 
n 
ii 
ii 

12 

io.  28191 

28171 

28150 
28130 
28109 

9-  7«732 
78760 

78789 
78817 

78845 

14 

IS 
15 

1  6 
16 

10.  21268 
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io.  06923 
06931 

06939 
06947 
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4 
4 
4 
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9-  93077 
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93°53 
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3° 
29 
28 

27 
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39 

7  47  20 
47  12 

47  4 

46  56 
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4  12  40 

12  48 
12  56 

13  4 

13  12 

9.71911 

71932 
71952 

71973 
71994 

12 
12 
13 
13 
13 

io.  28089 

28068 
28048 
28027 
28006 

9.  78874 
78902 
7393o 
78959 
78987 

17 
17 
17 

18 
18 

io.  21126 
21098 
21070 
21041 
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10.  06962 
06970 
06978 
06986 
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5 
5 

5 
5 

5 

9-  93038 
93030 
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25 
24 
23 

22 
21 

40 
4i 

42- 
43 
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7  46  40 
46  32 
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4  13  20 

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13  44. 
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9.  72014 

72034 
72055 
72075 
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14 
14 
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15 

io.  27986 
27966 

2/945 
27925 
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9.  79015 

79°43 
79072 
79100 
79128 

19 
19 
20 
20 

21 

io.  20985 

20957 

20928 
20900 

26872 

io.  07001 
07009 

07017 

07024 

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5 
5 

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6- 

9-  92999 
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92983 
92976 
92968 

20 
19 

18 

17 
16 

4£ 
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47 
48 

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7  46  o 
45  52 

45  44 
45  36 
45  28 

4  14  o 
14  8 
14  16 
14  24 

14  32 

9.  72116 
72137 
72157 
72177 
72198 

15 
16 
16 
16 
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io.  27884 
2/863 

2/843 
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9.  79156 
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79213 
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79269 

21 
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22 
23 
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10.  2084.). 
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10.  07040 
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6 
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9.  92960 

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15 
14 
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12 
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5' 
52 
53 
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14  48 
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15  12 

9.  72218 
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72259 
72279 
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17 
18 
18 
18 
19 

10.  27782 

27762 
27741 
27721 
27701 

9-  79297 
79326 
79354 
79382 
79410 

24 
24 
25 
25 
26 

io.  20703 

20674 
20646 
20618 
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10.  07079 
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07095 
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6 
7 
7 
7 
7 

9.92921 

92913 
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IO 
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59 
60 

7  44  40 

44  32 
44  24 
44  16 
44  8 
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4  15  20 
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15  52 
16  o 

9-  7232° 
72340 
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72401 
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20 
20 
20 
21 

10.  27680 
27660 

27640 
27619 
27599 
27579 

9-  79438 
79466 

79495 
79523 
79551 
79579 

26 
26 
27 

11 
28 

io.  20562 

20534 
20505 
20477 
20449 
20421 

io.  07119 
07126 

07134 
07142 
07150 
07158 

7 
.7 
7 

I 

8 

9.92881 
92874 
92866 
92858 
92850 
92842 

S 
4 
3 

2 
I 
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M. 

Hour  i1.  M. 

Hour  A.  M. 

Cosine. 

DI«. 

Secant. 

CousngeffL 

Diff. 

Tingent. 

Cococtint. 

Diff. 

Sine. 

M, 

121°                                                        58° 

SINES,  TANGENTS,  AND  SECANTS. 

32°                             .         _      _           1«° 

M. 

Hour  A.M. 

Hour  p.  M. 

Sine. 

Difl. 

Cosecant. 

Tangent. 

Did. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

I 

2 

3 
•  4 

7  44  o 
43  52 
43  44 
43  36 

43  28 

4  16  o 
16  8 
16  16 
16  24 
16  32 

9-  72421 
72441 
72461 
72482 
72502 

o 
o 

I 
I 

10.27579 
27559 
2/539 
27518 
27498 

9-  79579 
79607 

79635 
79663 
79691 

O 

o 

I 
I 

2 

10.  20421 

20393 
20365 

20337 
20309 

10.  07158 
07166 
07174 
07182 
07190 

o 
o 
o 
o 
I 

9.  92842 
92834 
92826 
92818 
92810 

60 

59 
53 
57 
56 

6 

8 
9 

7  43  20 
43  '2 
43  4 
42  56 
42  48 

4  16  40 
16  48 
16  56 
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9.  72522  , 
72542 
72562 
72582 
72602 

2 
2 

2 

3 
3 

10.  27478 
27458 
27438 
27418 
2739S 

9-  797'9 
79747 
79776 
79804 
79832 

2 

3 
3 
4 

4 

10.  20281 

20253 

20224 
20196 
20168 

10.  07197 
07205 
07213 
07221 
07229 

9.  92803 

92795 
92787 
92779 
92771 

55 
54 
53 
52 
5' 

10 

ii 

12 
13 

'4 

7  42  40 

42  32 

42  24 
42  16 
42  8 

4  '7  20 

17  28 

17  36 
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17  52 

9.  72622 

72643 
72663 
72683 
72703 

3 
4 
4 
4 
5 

10.  27378 

27357 
27337 

273'7 
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9.  79860 
79888 
79916 
79944 
79972 

5 

6 
6 

7 

10.  20140 

201  12 

20084 
20056 
20028 

10.07237 
07245 

07253 
07261 
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2 
2 
2 

9  .92  76  j 
92755 
92747 
92739 
92731 

5° 
49 
48 

4l 
46 

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16 
17 

19 

7  42  o 

41  52 
41  44 

41  36 

41  28 

4  18  o 
18  8 
18  16 
18  24 
18  32 

9-  72723 
72743 

72763 
72783 
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5 

I 
6 
6 

10.  27277 
27257 

27237 
27217 
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9.  80000 
80028 
80056 
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7 

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8 
9 

IO.  20OOO 
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19944 
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10.07277 

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2 
2 
2 
2 
3 

9-  92723 
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92707 
92699 
92691 

45 
44 
43 
42 
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20 

21 

22 
23 
24 

7  41  20 

41  12 

41  4 

40  56 
40  48 

4  18  40 
18  48 
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19  4 

19  12 

9-  72823 

72843 
72863 
72883 
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7 
7 

I 
8 

10.27177 
27157 
27137 
27117 

27098 

9.  80140 
80  1  63 
80195 
80223 
80251 

9 

10 

10 

II 
II 

10.  19860 

19832 

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10.07317 
07325 
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07349 

3 
3 
3 
3 
3 

9-  92683 
92675 
92667 
92659 
92651 

40 
39 
38 
37 
36 

26 
27 
28 
29 

7  4°  4° 
40  32 
40  24 
40  16 
40  8 

4  19  20 

19  28 
19  36 

19  44 
19  52 

9.  72922 
72942 
72962 
72982 
73002 

8 
9 
9 
9 

10 

10.  27078 

27058 
27038 

27018 
26998 

9.  80279 
80307 

80335 
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12 
12 
13 

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10.  19721 

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19665 

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10.07357 
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07381 

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3 
3 

4 
4 
4 

9.  92643 

92635 
92627 
92619 
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35 
34 
33 
32 
3' 

3° 
3' 
32 
33 
34 

7  40  o 
39  52 
39  44 
39  36 

39  28 

4  20  o 

20   8 
20  l6 

20  24 

20  32 

9.  73022 

7304i 
73061 
73081 
73101 

10 

10 
II 
ii 
ii 

to.  26978 

26959 
26939 

26919 

26899 

9.  80419 
80447 
80474 
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14 
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16 

10.  19581 

19553 
19526 
19498 
19470 

10.  07397 

07405 

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4 
4 
4 

4 
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9.  92603 

92595 
92587 

92579 
92571 

30 
29 
28 

27 
26 

35 
36 

H 
39 

7  39  20 
39  12 
39  4 
38  56 
38  48 

4  20  40 

20  48 
20  56 
21   4 
21  12 

9.  73121 

73140 
73160 
73180 
73200 

12 
12 
12 
'3 
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10.  26879 
26860 
26840 
26820 
26800 

9.  80558 
80586 
80614 
80642 
80669 

16 

17 
17 
18 
18 

10.  19442 

19414 
19386 
19358 

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10.  07437 

07445 
07454 
07462 
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5 
5 
5 
5 
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9-  92563 
92555 
92546 

92538 
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25 
24 
23 

22 
21 

40 
4' 
42 
43 
44 

7  38  4° 
38  32 
38  24 
38  16 
38  8 

4  21  2O 
21  28 
21  36 

21  44 

21  52 

9.  73219 
73239 
73259 
73278 
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13 
H 

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10.  26781 
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26741 

26722 
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9.  80697 
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19 

19 
20 
20 

20 

10.  19303 
19275 
19247 
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10.  07478 
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6 
6 
6 

9.92522 

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92506 
92498 
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2O 

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4I 
46 

47 
48 

49 

7  3»  o 
37  52 
37  44 
37  36 
37  28 

4  22   0 
22   8 
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22  24 
22  32 

9-  733  '8 
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73357 
73377 
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16 
16 
16 

10.  26682 

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9.  80836 
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80947 

21 
21 
22 
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10.  19164 

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19108 
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10.  07518 

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6 
6 
6 
6 
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9.  92482 
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92465 
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92449 

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12 
II 

5° 
5' 

52 
53 
54 

7  37  20 
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37  4 
36  56 
36  48 

4  22  40 
22  48 
22  56 

23  4 

23  12 

9-  734  «6 
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17 
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17 
18 
18 

10.  26584 

26565 
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9-  8°975 
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81030 
81058 
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23 
24 
24 
25 
25 

10.  19025 
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18942 
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10.07559 
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07575 
07584 
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7 
7 
7 
7 
7 

9-  9244! 
92433 
92415 
92416 

92408 

10 
I 
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55 
56 

11 

59 
60 

7  36  4° 
36  32 
36  24 
30  16 
36  8 
36  o 

4  23  20 

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23  36 

23  44 
23  52 
24  o 

9.735:3 
73533 
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73572 
73591 
73611 

lo1 
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19 
19 

20 
20 

10.  26487 
26467 
26448 

26428 

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9.81113 
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81224 
81252 

26 
26 
26 
27 

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10.  18887 

18059 
18831 

181:04 

18775 

18748 

10.  07600 
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07616 
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8 
8 
8 
8 

9.  92400 
92392 
92384 
93370 

92367 

92359 

5 
4 
3 

2 

I 
0 

M. 

Hour  P.  M. 

Hour  A.M. 

Cosine. 

Dlff 

Secant. 

Cotangent. 

DIP. 

T?.ngt;nt.. 

Coeswnt. 

Dlff. 

Sine. 

M, 

122°                                                          57° 

210 


SINES,  TANGENTS,  AND  SECANTS. 
33°                                                                                                                                                 116° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

DiSf 

Cosine. 

M. 

0 

I 

2 

3 
4 

7  36    ° 
35  52 
35  44 
35  36 
35  28 

4  24     o 
24    8 
24  16 

24  24 
24  32 

9.  7361  1 
73630 

7365° 
73669 

73689 

0 

o 
I 
I 
I 

10.  26389 
26370 
26350 

26331 
26311 

9.81252 

81279 
81307 

8J335 
81362 

O 
o 

i 
I 

2 

10.  18748 
18721 
18693 
18665 
18638 

10.07641 
07649 
07657 
07665 
07674 

O 
0 

o 
o 
1 

9-  92359 
92351 
9*343 
92335 
92326 

60 

59 
58 
57 
56 

6 

I 

o 

7  35  20 
35  '2 
35    4 
34  56 
34  48 

4  24  40 
24  48 
24  56 
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25    12 

9-  73708 
73727 
73747 
73766 

73785 

2 
2 
2 
3 
3 

10.  26292 
26273 
26253 
26234 
26215 

9-  81390 
81418 
8144-5 

81473 
81500 

2 

3 
3 
4 

4 

10.  18610- 

18582 

'8555 
18527 

18500 

10.  07682 
07690 
07698 
07707 
07715 

9.  92318 
92310 
92302 

92293 

92285 

55 
54 
5? 
52 
5i 

10 

ii 

12 
S3 
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7  34  4° 
34  32 
34  24 
34  '6 
34    8 

4  25  20 

25    23 
25   -3° 

25  44 
25  52 

9.  75805 
73824 
73843 
73863 

73882 

3 

3 
4 
4 
4 

10.26195 
26176 
26157 
26137 
26118 

9.81528 
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81583 
81611 
81638 

5 

5 

0 

6 

10.  18472 
18444 
18417 
18389 
18362 

10.07723 

0773« 
07740 

07748 
07756 

I 

2 
2 
2 
2 

9.92277 
92269 

92260 
92252 
92244 

So 
49 
48 

47 
46 

.11 

11 
19 

7  34r   o 
33  52 
33  44 
33  36 
33  28 

4  26    o 
26    8 
26  J6 
26  24 

26  32 

Q.  73901 
73921 
73940 

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Hour  A.M. 

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M. 

123°                                                                                                                                                       56° 

SINES,  TANGENTS,  AND  SECANTS. 
34°                                                                                                                                                      145° 

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10.  24964 

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9.  91686 

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Hour  A.  M. 

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M. 

124°                                                                                                                                                       55° 

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16 
16 

10.  21147 

2II3I 
2II14 
21098 
21082 
2IO&6 

9.89151 
89177 
89203 
89229 
89255 

SgCtii 

24 
24 
25 
25 
26 
26 

10.  10849 

10823 
10797 
10771 
10745 

10^19 

10.  10298 
10307 
10317 
10327 
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i°347 

9 
9 
9 
9 

10 
10 

9.  89702 
89693 
89683 

896/3 
89663 

89653 

5 
4 
3 

2 
I 
O 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine.     1  Diff. 

Secant. 

Colan£eut. 

Din. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

1£J°                                                                                                                                                                             52° 

215 


SINES,  TANGENTS,  AND  SECANTS. 

38°                                                                                                                                  .                                m° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sice. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

O 

I 

2 

3 

4 

6  56    o 

55  52 
55  44 
55  36 
55  28 

540 

4    8 
4  16 

4  24 

4  32 

9-  7S934 
78950 
78967 
78983 
78999 

O 
O 

I 
I 
I 

10.  21066 
21050 
21033 
21017 
2IOOI 

9  89281 
89307 
89333 
89359 
89385 

O 

o 
I 
I 

2 

10.  10719 

10693 
10667 
1064! 

10615 

10.  10347 

I°357 
10367 
10376 
10386 

O 
O 
0 

9-  89653 
89643 

%633 
89624 
89614 

60 
59 
58 
57 
S6 

6 

8 
9 

6  55  20 
55  12 
55    4 
54  56 
54  48 

5    4  40 
448 
4  56 
5    4 

5    '2 

9-  79°'  5 
79°3' 
79047 
79063 
79°'/9 

I 

2 
2 

2 
2 

10.  20985 

20969 

20953 
20937 
20921 

9.89411 
89437 
89463 
89489 
89515 

2 

3 
3 
3 

4 

10.  10589 

10563 

>°537 
10511 

10485 

lo.  10396 
10406 
10416 
10426 
10436 

2 

9.  89604 
89594 
89584 

89574 
89564 

55 
54 
53 
52 
SI 

10 

II 

12 
13 
14 

6  54  40 
54  32 
54  24 
54  '6 
54     8 

5    5  20 
528 
5  36 
5  44 
5  52 

9-  79°95 
79111 
79128 

79144 
79160 

3 

3 

3 
4 

10.  20905 
20889 
20872 
20856 
20840 

9.  89541 
89567 
89593 
89619 

89645 

4 
5 

1 

6 

10.  10459 

10433 
10407 
10381 
i°355 

10.  10446 
10456 
10466 
10476 

10486 

2 

2 
2 
2 
2 

9-  89554 
89544 

89534 
89524 
89514 

5° 
49 

47 
46 

>5 
16 

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6  54     o 
53  52 
53  44 
53  36 
53  28 

560 
6    8 
6  16 
624 
6  32 

9.79176 
79192 
79208 
79224 
79240 

4 
4 
5 
5 

5 

10.  20824 

20808 

20792 

20776 

20760 

9.  89671 
89697 

89723 
89749 

89775 

b 

7 

8 
8 

10.  10329 

103°3 
10277 
10251 
10225 

10.  10496 

10505 
10515 
10525 

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3 
3 

3 
3 
3 

9-  89504 
89495 
89485 

89475 
89465 

45 
44 
43 
42 
4' 

20 

21 
22 
23 
24 

6  53  20 
53  12 

53    i 

52  56 

52  48 

5    6  40 
6  48 
6  56 

7    4 

7  12 

9-  79256 
79272 
79288 
793°4 
793  '9 

6 

6 
6 

10.  20744 
20728 
2071? 
20696 

20681 

9.  89801 
89*27 
89853 
89879 
89905 

9 
9 

10 
10 
IO 

lo.  10199 
10173 
10147 
IOI2I 

10095 

10.  10545 

'0555 
10565 

10575 

10585 

3 
4 
4 
4 
4 

9.  89455 
89445 
89435 
89435 
89415 

40 
39 

I 

25 
26 

27 
28 
29 

6  52  40 
52  32 
52  24 
52  16 

52     8 

5     7  20 
7  28 
7  36 
7  44 
7  52 

9-  79335 
79351 
79367 
79383 
79399 

7 

7 
7 
7 
8 

10.  20665 
20649 
20633 
20617 
20601 

9-  89931 
89957 
89983 
90009 
90035 

11 
II 

12 

12 

«3 

10.  10069 
10043 
10017 
09991 
09965 

10.  10595 
10605 
10615 
10625 
10636 

4 
4 

5 
5 
S 

9-  89405 
89395 
89385 

89375 
89364 

35 
34 
33 
32 
3i 

3° 

31 

32 

33 

34 

6  52    o 

51  52 
51  44 
5'   36 
51  28 

580 
8    8 
8  16 
8  24 
832 

9-  794'5 
7943' 
79447 
79463 
79478 

8 
8 
8 
9 
9 

10.  20585 
20569 

20553 
20537 

20522 

9.  90061 
90086 
90112 
90138 
90164 

'3 
'3 
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H 
15 

10.  09939 

09914 
09888 

09862 
09836 

10.  10646 
10656 
10606 
10676 
10686 

5 
5 

6 

9-  89354 
89344 
89334 
89324 
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30 

28 

27 
26 

35 
36 

37 
38 

39 

6  51  20 

51    12 

51     4 

5°  56 
50  48 

5    8  40 
8  48 
8  56 

9    4 
9  12 

9-  79494 
79510 
79526 
79542 
79558 

9 

10 
10 

10 
10 

10.  20506 
20490 

20474 
20458 
20442 

9.  90190 
90216 
90242 
90268 
90294 

15 
16 
16 
16 
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10.  09810 

09784 
09758 
09732 

09706 

10.  10696 
10706 
10716 
10726 

10736 

6 
6 
6 

6 

7 

9-  89304 
89294 
89284 

89274 
89264 

25 
24 
23 

22 

21 

40 
41 
42 
43 
44 

6  50  40 

5°  32 
50  24 
50  16 
50    8 

5    9  20 
9  28 
9  36 
9  44 
9  52 

9-  79573 
79589 
79605 
79621 
79636 

II 
II 
II 
II 

12 

10.  20427 
20411 

20395 
20379 
20364 

9.  90320 
90346 
90371 
90397 
90423 

17 
18 
18 
19 
19 

10.  09680 

09654 

09629 

09603 
09577 

10.  10746 

10756 
10767 

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7 
7 
7 
7 
7 

9-  89254 
89244 
89233 
89223 
89213 

2O 
19 

18 

17 

16 

45 

44 
47 

48 
49 

6  50    o 
49  52 
49  44 
49  36 
49  28 

5  10    o 
10    8 
10  16 
10  24 

10  32 

9.  79052 
79668 
79684 
79699 
79715 

12 
12 
12 
'3 

M 

10.  20348 
20332 
20316 
20301 
20285 

9.  90449 

90475 
90501 

90527 
90553 

19 
20 

20 
21 
21 

10.  09551 

09525 

09499 

09473 
09447 

10.  10797 
10807 
10817 
10827 
10838 

8 
8 
8 
8 
8 

9.  89203 

89193 
89183 

89173 

89762 

15 
14 
13 

12 
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5° 
5' 

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53 
5^ 

6  49  20 
49  12 

49     4 
48  56 
48  48 

5  10  40 

10   48 

10  56 
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9-  7973' 
79746 
79762- 
79778 
79793 

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14 
14 

14 
H 

10.  20269 
20254 
20238 

20222 
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9.90578 
90604 
90630 
90656 
90682 

22 
22 
22 
23 
23 

10.  09422 

09396 
09370 
09344 

09318 

10.  10848 
10858 
10868 
10878 
10888 

8 
9 
9 
9 
9 

9.  89152 
89142 
89132 
89122 
89112 

IO 

6 

5S 
56 
57 
5« 
59 
60 

6  48  40 

48  32 
48  24 
48  16 
48    8 
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5    II    20 
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II    36 

II  44 
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12      O 

9-  79^09 
79825 
79840 
79856 
79872 
79887 

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15 

IS 

11 

16 

10.  20191 

20175 
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20144 
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9.  90708 

90734 
90759 
90785 
90811 
90837 

24 
24 
25 

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26 

10.  09292 
09266 

09241 
09215 
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IO.  10899 
10909 

10919 
10929 

10940 
10950 

9 
9 

10 
IO 
IO 
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9.  89101 
89091 
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89071 
89060 
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5 
4 
3 

2 
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0 

M. 

Hour  p.  M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

128°                                                                                                                                                         51° 

310 


SINES,  TANGENTS,  AND  SECANTS. 
39°                                                                1  J0° 

M. 

Hour  A.M. 

Hour  !•.  tl. 

Sine. 

DilT. 

Cosecant, 

Tangent. 

DilT 

Cotangent. 

Secant. 

Diff. 

Cosine 

M. 

o 
•i 

2 

3 

4 

6  48  o 
47  S2 
47  44 
47  36 
47  28 

5  12  o 

12   8 

12  16 
12  24 

12  32 

9-  79SS7 

799°3 

79918 

79934 

79950 

o 
o 
I 
I 
I 

10.  20113 
20097 
200^2 
2O066 
20050 

9-90S37 
90863 
90889 
90914 
90940 

o 
o 

I 
I 

2 

10.  09163 

09'37 
09111 

09086 

09060 

10.  10950 
logSo 

10970 
10980 
10991 

O 

o 
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9.  89050 
89040 
89030 
89050 
89069 

60 
59 

58 

si 

I 

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9 

6  47  20 
47  «2 
47  4 
46  56 
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5  '2  4° 
12  48 
12  56 

13  4 

13  12 

9-  799'J5 
79981 
79996 

OOO  1  2 

80027 

I 

2 

2 
2 
2 

10.  20035 

20019 
20004 
19988 
19973 

9.  90966 
90992 
91018 

9  '043 

91069 

2 

3 
3 
3 
4 

10.  09034 
09008 

08982 

08957 
08931 

10.  I  1001 
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2 

9-  88999 
88989 
88978 
88968 

88958 

55 
54 
53 
52 
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10 

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12 
13 
14 

6  46  40 

46  32 
46  24 
46  16 
46  8 

5  '3  20 

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13  36 

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9-  8o°43 
80058 
80074 
80089 
80105 

3 
3 
3 
3 

4 

10.  19957 

19942 
19926 
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19895 

9.91095 
91121 

91  '47 
91172 
91198 

4 
5 

6 

10.  08905 
08879 

08853 
08828 
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10.  11052 

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11083 
11094 

2 
2 
2 
2 
2 

9.  88948 

88937 
1,8927 
88-917 

88906 

5° 
49 
48 
47 
46 

15 

1  6 

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6  46  o 
45  52 
45  44 
45  36 
45  28 

5  14  o 
14  8 
14  16 
14  24 
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9.  80120 
80136 
80151 
80166 
80182 

4 

4 
4 
5 
5 

10.  19880 

19864 

19849 

19834 
19818 

9.91224 
91250 
91276 
91301 
91327 

6 
7 

8 

10.  08776 

08750 
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08699 

08673 

io.  11104 
11114 
11125 

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11145 

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3 
3 
3 

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9.  88896 
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88865 
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45 
44 
43 
42 
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20 
21 
22 

23 

24 

6  45  20 
45  12 
45  4 

44  56 

44  48 

5  '4  4° 
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14  56 

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15  12 

9.  80107 
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80244 
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5 

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6 
6 

10.  19803 

19787 
19772 
19756 
19741 

9-91353 
91379 
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9  '43° 

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9 
9 
9 
10 

10 

10.  08647 
08621 
08596 
08570 
08544 

io.  11156 
11166 
11176 
11187 
11197 

3 
4 
4 
4 

4 

9.88844 
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88824 
88813 
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40 

51 

35 

37 
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25 
26 

287 

29 

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44  32 
44  24 
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44  8 

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15  28 

15  36 

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15  52 

9.  80274 
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80305 
80320 
80336 

6 
7 
7 
7 
7 

lo.  19726 

19710 
19695 

19680 

19664 

9.  91482 
91507 

9'533 
9'559 

91585 

II 
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12 

12 
12 

10.08518 

08493 
08467 
08441 
08415 

10.  11207 

11218 
11228 
11239 

11249 

4 
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5 

5 

9.  .88  793 
88782 
88772 
88761 
88751 

35 
34 
33 
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3° 
3' 
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33 
34 

6  44  o 
43  52 
43  44 

V  36 

43  28 

5  16  o 
16  8 
16  16 
16  24 
16  32 

9-  80351 
80366 
80382 

80397 
80412 

8 
8 
8 
8 
9 

10.  19649 

19634 
19618 

19603 

19588 

9.  91610 
91636 
91662 
91688 
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13 

13 

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IS 

10.  08390 
08364 
08338 
08312 

08287 

io.  11259 
11270 
11280 
11291 
11301 

5 

0 

6 
6 

9.  88741 
88730 
88720 
88709 
88699 

3° 
29 
28 

27 

26 

35 
36 

P 

39 

6  43  20 
43  >2 
43  4 

42  s6 

42  48 

S  io  40 
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16  56 
17  4 

17  12 

9.  80428 
80443 
80458 
80473 
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9 
9 
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10 
10 

10.  19572 

19557 
19542 
19527 
19511 

9-9"739 
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91791 
91816 
91842 

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15 

1  6 
16 

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10.  08261 
08235 
08209 
08184 
08158 

io.  11312 
11322 

11332 

M343 
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6 
6 
6 
7 
7 

9.  8S6S8 
88678 
8S668 
88657 
88647 

25 
24 
23 

22 
21 

40 
41 
42 
43 

44 

6  42  40 
42  32 
42  24 
42  16 
42  8 

5  '7  20 
17  28 

17  36 

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9.  80504 
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80534 
80550 
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10 

10 
II 
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10.  19496 

19481 
19466 

19450 
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9.  91868 

9  1893 
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9  '945 

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18 
18 
18 

'9 

10.  08132 
08107 

08081 

08055 

08029 

io.  11364 
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11406 

7 

7 
7 
7 
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9.  88636 
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88605 
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19 

18 

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45 
46 

47 

48 

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6  42  o 

42  52 
41  44 

41  36 
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5  18  o 
18  8 
18  16 
18  24 
18  32 

9.  80580 
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80610 
80625 
80641 

12 
12 
12 
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10.  19420 
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9.91996 
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92048 
92073 
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20 
20 
21 
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10.  08004 

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io.  11416 
11427 

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11448 
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8 
8 
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8 
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9.  8^584 

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15 
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12 
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52 
53 
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6  41  20 

41  12 

41  4 
40  56 

40  48 

5  18  40 
18  48 
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19  4 

19  12 

9.  80656 
80671 
80686 
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13 
13 
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10.  19344 
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9.92125 
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92176 
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10.  07875 
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07798 
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io.  11469 

11479 
11490 
11501 
11511 

9 
9 
9 
9 
9 

9.88531 
88521 
88510 
88499 
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40  32 
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19  28 
19  36 

19  44 

19  52 

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9-  8°73' 
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80762 
80777 
80792 
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14 
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15 
15 
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10.  19269 
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19238 
19223 
19208 
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9.  92253 
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24 
24 
24 
25 

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26 

10.  07747 

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07696 
07670 
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io.  11522 

11532 

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9.  88478 
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5 
4 
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2 
1 
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M. 

Hour  v,  M. 

IIourA.M. 

Cosine 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecani,. 

Diff. 

Sine. 

M. 

129°                                                             50° 

317 


SINES,  TANGENTS,  AND  SECANTS. 
40'                                                            -   139° 

M. 

Hour  A.  M. 

Ho\ir  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 
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2 

3 

4 

6  40  o 

39  52 

39  44 
39  36 
39  28 

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20  8 
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20  24 

20  32 

9.  80807 
80822 
80837 
80852 
80867 

0 
0 

0 

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19178 
19163 
19148 
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9-  923SI 
92407 

92433 
92458 
92484 

O 
O 
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2 

IO.  07619 

07593 
07567 
07542 
07516 

io.  11575 

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11596 
11606 
11617 

0 
0 

o 

9.  88425 
88415 
88404 

88394 
88383 

60 

59 

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6 

8 
9 

6  39  20 
39  12 
39  4 
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5  20  40 
20  48 
20  56 
21   4 
21  12 

9.  80882 
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80912 
80927 
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2 
2 
2 

10.  19118 

19103 
19088 
19073 
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9.92510 

92535 
92561 

92587 
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3 
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4 

io.  07490 
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io.  11628 

11638 
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9-  88372 
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88351 
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88330 

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54 
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12 

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6  38  40 
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5  21  20 
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3 
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10.  19043 
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9.  92638 
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9.88319 
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88298 
88287 
88276 

5° 
49 

48 

47 
46 

15 

16 

17 

18 
19 

6  38  o 
37  S2 
37  44 
37  36 
37  28 

5  22   O 
22   8 
22  16 
22  24 
22  32 

9.  81032 
81047 
81061 
81076 
81091 

4 
4 
4 
4 

5 

10.  18968 

18953 
18939 
18924 

18909 

9.  92766 
92792 
92817 
92843 
92868 

6 

7 
7 
8 
8 

io.  07234 
07208 
07183 
07i57 
07132 

io.  11734 

11745 
11756 

1  1  766 
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3 
3 
3 
3 
3 

9.  88266 
88255 
88244 
88234 
88223 

45 
44 
43 
42 
41 

20 
21 
22 

23 

24 

6  37  20 
37  12 
37  4 
36  56 
36  48 

5  22  40 
22  48 
22  56 
23   4 
23  12 

9.  8  1  106 
81121 
81136 
81151 

81166 

5 
5 

6 
6 

10.  18894 

18879 
18864 
18849- 
18834 

9.  92894 
92920 

92945 
92971 
92996 

9 
9 
9 

10 
10 

io.  07106 
07080 

07055 

07029 

07004 

ID.  11788 

11799 

11809 
11820 

11851 

4 
4 
4 
4 
4 

9.  88212 
88201 
88191 
'SSiSo 
88169 

40 
39 

38 
37 
3° 

11 

27 
28 

29 

6  36  40 

3f>  32 

36  24 

36  16 
36  8 

5  23  20 
23  28 
23  36 

23  44 

23  52 

9.  S  1  1  80 
81195 
81210 
81225 

81240 

6 
6 
7 
7 
7 

10.  18820 

18805 
18790 
18775 

18760 

9.  93022 
93048 

93°73 
93°99 
93  124 

ii 

II 

12 
12 
12 

io.  06978 
06952 
06927 
06901 

06876 

io.  11842 
11852 
11863 

11874 

1  1  S»j 

4 
5 

5 
S 

5 

9.  88158 
88148 
88137 
88126 
88115 

35 
34 
33 
j2 
3' 

3° 
3' 
32 

33 
34 

6  36  o 

35  52 

35  44 
35  36 
35  28 

5  24  o 
24  8 
24  16 
24  24 

24  32 

9.81254 
81269 
81284 
81299 
81314 

8 
8 
8 
8 

lo.  18746 

18731 

18716 
18701 
18686 

9.93150 

93  '75 
93201 

93227 
93252 

13 
13 
14 
'4 
14 

Io.  06850 

06825 
06799 
06773 

06748 

io.  11895 
11906 

1,1917 
1  1928 

I  '939 

I 

6 
6 
6 

9.88105 
88094 
88083 
88072 
88061 

3° 
29 

28 

27 
26 

35 
36 
37 
38 

39 

6  35  20 
35  12 
35  4 
34  56 
34  48 

5  24  40 
24  48 
24  56 
25  4 

25  12 

9.  81328 

8i343 
81358 

S'372 
81387 

9 

9 
9 
9 

10 

io.  18672 

18657 

18642 
18628 
18613 

9.93278 
933<>3 
93329 
93354 
9338° 

15 

15 
16 
16 
17 

io.  06722 
06697 
06671 
06646 
06620 

ION  11949 
1  1960 
11971 
11982 
1  1  993 

6 
6 
7 
7 
7 

9.  88051 
88040 
88029 
88018 
88007 

25 
24 

2j 
22 
21 

40 
4' 
42 
43 

44, 

6  34  40 
34  32 
34  24 
34  "6 

34  8 

5  25  20 
25  28 

25  36 
25  44 
25  52 

9.  81402 
81417 
81431 
81446 
81461 

10 

10 
10 

II 

II 

io.  18598 

18583 

18569 
18554 
18539 

9.  93406 
93431 
93457 
93482 
935°8 

17 
17 
18 
18 

•9 

IO.  06594 

06569 

06543 

06518 
06492 

10.  12004 
12015 
12025 
12036 

12047 

7 

8 
8 
8 

9-  8799A 
87985 

879-75 
87964 
87953 

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iS 

'7 
16 

45 
46 

47 
48 

49 

6  34  o 
33  52 
33  44 
33  36 
33  28 

5  26  o 
26  8 
26  16 
26  24 

26  32 

9.81475 
81490 
81505 
81519 
81534 

II 
II 

12 
12 
12 

10.  18525 
18510 
18495 
18481 
18466 

9-  93533 
93559 
93584 
93610 

93636 

19 

20 
20 
20 
21 

io.  06467 

06441 

06416 
06390 

06564 

io.  12058 
12069 

I2oSo 
I209I 
1  2  1  02 

8 
8 
8 
9 
9 

9-  87942 
87931 
87920 
87909 
87898 

'5 
>4 
'3 

12 
I  I 

5° 

5' 
5- 
53 
54 

6  33  20 
33  12 
33  4 

32  56 
32  48 

6  26  40 
26  48 
26  56 

27  4 
27  12 

9-  8'549 
81563 
8I578 
81592 
81607 

12 
'3 

'3 
13 
13 

io.  18451 

"8437 

18422 
18408 

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9.  93"6i 
93687 
93712 
9373s 
93763 

21 
22 
22 
23 

IO.  06339 

°6,3  13 

06288 

06262 
06237 

10.  124  1  3 

I2I23 

12134 
I2I45 
12,56 

9 
9 
9 

10 
IO 

9.  87887 
87877 
87866 

87S55 
87844 

10 

9 
S 

7 
6 

55 
56 

ii 

59 
60 

6  32  40 

32  32 
32  '24 
32  16 
32  8 
32  o 

5  27  20 
27  28 

27  36 

27  44 
27  52 
28  o 

9.  81622 
81636 
81651 
81065 
81680 
81694 

H 

'4 
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H 

15 

15 

io.  18378 

18364 
18349 

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18320 
18306 

9-93/89 
93814 
93840 

93865 
93891 
93916 

23 
24 

24 

25 
25 

26 

io.  062  r  i 
06186 
06160 
06135 
06109 
06084 

Io.  12107 
12178 
121X9 

12200 
I22II 
12222 

IO 
IO 
IO 
10 

II 
II 

9-  87833 
87822 
87811 
87800 
87789 
87778 

5 
4 
3 

2 
I 
o 

M. 

Hour  r.  M 

HoUFA.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

biff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

130°                                                                   4»° 

218 


SINES,  TANGENTS,  AND  SECANTS. 
41°                                                                                                                                                                  138° 

M. 

Hour  A.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cobccant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

o 
I 
2 

3 
4 

6  32     o 
3«    52 
3'   44 
3>  36 
3«  28 

5  28    o 
28    8 
28  16 
28  24 
28  32 

9.  81694 
81709 
81723 
81738 
81752 

O 
O 
O 
I 
I 

IO.  18306 
18291 
18277 
18262 
18248 

9-  939'6 
93942 
93967 
93993 
94018 

O 
O 
I 
I 

2 

IO.  06084 
06058 
06033 
06007 
05982 

10.  12222 
12233 
12244 
12255 
12266 

0 
O 
O 

9.  87778 
87767 
87756 
87745 
87734 

60 
59 
58 

57 
56 

I 

8 
9 

6  31  20 

31    12 

31      i 
30    56 

30   48 

5  28  40 
28  48 
28  56 
29     4 

29    12 

9.81767 
81781 
81796 
81810 
81825 

I 
I 

2 
2 
2 

10.  18233 
18219 
18204 
18190 

18175 

9.  94044 
94069 
94095 
94120 
94146 

2 

3 
3 
3 
4 

10.05956 
05931 

°59°5 
05880 

05854 

10.  12277 

12288 
12299 
I23IO 
12321 

2 

9-  87723 
87712 
87701 
87690 
87679 

55 
54 
53 
52 
5' 

10 

II 

12 

'3 
'4 

6  30  40 

3°  S2 
30  24 
30  16 
30    8 

5    29    20 
29    28 
29    36 

29  44 
29  52 

9.81839 
81854 
81868 
81882 
81897 

2 

3 
3 
3 
3 

10.  18161 

18146 
18132 
18118 
18103 

9.94171 

94197 
94222 

94248 
942/3 

4 

5 

I 

6 

10.  05829 

05803 
05778 
05752 
05727 

10.  12332 

12343 
'2354 

12365 

12376 

2 
2 
2 
2 
3 

9.  87668 
87657 
87646 

87635 
87624 

5° 
49 
48 

47 
46 

15 
16 

'7 
18 

'9 

6  30    o 
29  52 
29  44 

29  36 
29  28 

5  3°     o 
30    8 

30  16 
30  24 
3°  32 

9.81911 
81926 
81940 

81955 
81969 

4 
4 
4 
4 
5 

lo.  18089 

18074 
18060 

18045 

18031 

9-  94299 
94324 
9435° 
94375 
94401 

6 
7 

8 
8 

10.  05701 
05676 
05650 

05625 
05599 

10.  12387 

12399 

12410 
12421 
12432 

3 

3 
3 
3 

4 

9.87613 
87601 
87590 

87579 
87568 

45 
44 
43 
42 

4' 

20 
21 
22 
23 
24 

6  29  20 

29    12 

29     4 

28  56 
28  48 

5  3°  4° 
30  48 
30  56 
31     4 

31    12 

9.  81983 
81998 
82012 
82026 
82041 

5 
5 
5 

0 

10.  18017 
18002 

17988 
17974 
17959 

9.  94426 
94452 
94477 
94503 
94528 

0 

9 
9 

10 
IO 

10.05574 
05548 
05523 
05497 
05472 

10.  12443 

12454 
12465 
12476 
12487 

4 
4 
4 
4 
4 

9-  87557 
87546 
87535 
87524 
87513 

40 
39 
38 
37 
36 

11 

27 
28 
29 

6  28  46 
28  32 
28  24 
28  16 
28     8 

5  3'  20 
31  28 

31  36 

3'  44 
3i  52 

9.  82055 
82069 
82084 
82098 
82II2 

6 
6 
6 

7 
7 

10.  17945 

1  793' 
17916 
17902 

17888 

9-  94554 
94579 
94604 

9463° 
94655 

ii 
ii 
ii 

12 
12 

10.  05446 

05421 
05396 
05370 
05345 

10.  12499 
12510 
12521 

12532 

12543 

5 

5 
S 

5 

5 

9.87501 
87490 

87479 
87468 

87457 

35 
34 
33 
32 
3l 

3° 
3i 
32 
33 
34 

6  28    o 
27  52 
27  44 
27  36 
27  28 

5  32     o 
32     8 
32  16 
32  24 
32  32 

9.  82126 
82141 
82155 
82169 
82184 

7 

8 

8 

10.17874 

17859 
17845 
17831 
17816 

9.  94681 
94706 
94732 
94757 
94783 

'3 
13 

«4 

H 
H 

10.  05319 

05294 
05268 

05243 
05217 

10.  12554 
12566 

12577 
12588 
12599 

6 
6 
6 
6 
6 

9.  87446 
87434 
8/423 
87412 
87401 

30 
29 
28 
27 

25 

35 
36 
37 
38 
39 

6  27  20 

27    12 

27     4 

26  56 
26  48 

5  32  40 
32  48 
32  56 
33    4 
33  12 

9.82198 
82212 
82226 
82240 
82255 

8 
9 
9 
9 
9 

10.  1  7802 

17788 

17774 
17760 

'7745 

9.  94808 
94834 
94859 
94884 
94910 

15 
15 
16 
16 
17 

10.  05192 
05166 

05141 
05116 

05090 

10.  12610 
12622 

12633 
12644 
12655 

7 
7 
7 
7 
7 

9-  8739° 
87373 
87367 
87356 
87345 

25 
24 
23 

22 
21 

40 
41 
42 
43 
44 

6  26  40 
26  32 
26  24 
26  16 
26     8 

5  33  20 
33  28 
33  36 
33  44 
33  52 

9.  82269 
82283 
82297 
82311 
82326 

10 
10 

IO 
10 
10 

10.17731 

I77I7 

17703 
17689 

17674 

9-  94935 
94961 
94986 
95012 
95037 

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17 
18 
18 
'9 

10.  05065 

05039 
05014 

04988 
04963 

10.  12666 
12678 
12689 
12700 
12712 

I 
8 
8 
8 

9-  87334 
87322 

8/3" 
87300 
87288 

20 

i3 

17 
16 

% 

8 

49 

6  26    o 
25  52 
25  44 
25  36 
25  28 

5  34    ° 
34    8 
34  16 
34  24 
34  32 

9.  82340 

82354 
82368 
82382 
82396 

II 
II 
II 
II 

12 

10.  17660 
17646 
17632 
17618 
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9.  95062 
95088 

95"3 
95139 
95164 

19 
20 
20 
20 

21 

10.  04938 
04912 
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04861 

04836 

10.  12723 

12734 
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8 
9 
9 
9 
9 

9.87277 
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15 
14 
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12 
II 

5° 
5> 
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53 
54 

6  25  20 

25    12 

25     4 
24  56 
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5  34  40 
34  48 
34  56 
35     4 
35  I2 

9.  82410 
82424 
82439 
82453 
82467 

12 
12 
12 
13 

y 

10.  17590 

17576 
17561 

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9.95190 
95215 
95240 
95266 
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21 
22 
22 
22 

23 

10.  04810 

04785 

04760 

04734 
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10.  12779 

12791 
12802 
12813 
12825 

9 

IO 
IO 
10 
10 

9.  87221 
87209 
87198 
87187 

871/5 

IO 

9 

& 

6 

55 
56 

9 

59 
60 

6  24  40 

24  32 
24  24 
24  16 
24    8 
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5  35  20 
35  28 
35  36 
35  44 
35  52 
36    o 

9.  82481 

82495 
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82523 

82537 
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23 
24 
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25 
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10.  04683 

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10.  12836 

12847 
12859 
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I  -88  1 
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10 
IO 

II 
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9.  87164 

87153 
87141 
87130 
87119 
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5 
4 
3 

2 
I 
O 

M. 

Hour  p  H. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

m°                                                                                                     48° 

SINES,  TANGENTS,  AND  SECANTS. 

42° 

137° 

M. 

HOUFA.  M. 

Hour  p.  M. 

Sine. 

Diff. 

Cosecant. 

Tangent. 

Diff. 

Cotangent. 

Secant. 

Diff. 

Cosine. 

M. 

0 

I 

.2 

3 
4 

6  24  o 
23  52 

23  44 
23  36 
23  28 

S360 
36  8 

36  16 
36  24 
36  32 

9.82551 
82565 
8*579 
82593 
82607 

O 
O 
O 
I 
I 

10.  17449 

'7435 
17421 
17407 
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9-95444 
95469 

95495 
95520 

95545 

O 
0 

I 

2 

10.  04556 

0453' 
04505 
04480 

04455 

10.  12893 

12904 
12915 
12927 
12938 

0 
0 

o 

9.87107 
'  87096 
87085 

870/3 

87062 

60 

P 

! 

6 
9 

6  23  20 

23  12 

23  4 

22  56 
22  48 

5  3°  4° 
36  48 

36  56 
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37  12 

9.  8262^ 
82635 
82649 
82663 

82677 

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2 
2 
2 

10.  17379 
17365 
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'7337 
17323 

9-9557' 
95596 

95622 

95647 
95672 

2 

3 

3 
3 
4 

10.  04429 
04404 
04378 

04353 
04328 

10.  12950 
12961 

12972 
12984 
12995 

2 

2 

9.  07050 

87039 
87028 
87016 

87005 

55 
54 
53 
52 
5' 

10 

ii 

12 

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H 

6  22  40 
22  32 
22  24 
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S  37  20 
37  28 
37  36 
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37  52 

9.  82691 
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82719 

82733 

82747 

2 
3 

3 

3 

3 

10.  1  7309 
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17281 
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9.95698 

95723 
95748 
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4 
5 
5 

1 

10.  04302 

04277 
04252 

04226 
04201 

10.  13007 
13018 

13030 
13041 

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2 
2 
2 

3 
3 

9-  86993 
86982 
86970 
86959 
86947 

5° 
49 
48 
47 
46 

15 
16 
17 
18 
IQ 

6  22   0 
21  52 

21  44 

21  36 
21  28 

5  &  ° 
38  8 
38  16 
38  24 
38  32 

9.  82761 

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82788 
82802 
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3 
4 
4 
4 
4 

10,  17239 

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17212 

17198 
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9-  95825 
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7 

1 

8 

10.  04175 

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10.  13064 

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3 
3 
3 
3 

4 

9.  86936 
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86902 
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45 
44 
43 
42 

41 

20 
21 
22 

23 
24 

6  21  2O 
2-1  12 

21   4 
20  56 
20  48 

5  38  40 
38  48 
38  56 
39  4 
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9.  82830 
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82858 

82872 
82885 

5 
5 
5 

6 

10.  17170 

17156 
17142 
17128 
17115 

9.  95952 

95977 
96002 
96028 
96053 

o 
9 
9 

10 
10 

10.  04048 
04023 
03998 
03972 

03947 

10.  13121 

13133 
13145 
13156 
13168 

4 
4 
4 
4 
5 

9.86079 
86867 
86855 
86844 
86832 

40 

39 
38 
37 
36 

25 
26 

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28 
29 

6  20  40 
20  32 
2O  24 

20  16 

20   8 

5  39  20 
39  28 
39  36 
39  44 
39  52 

9.  82859 

82913 
82927 
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6 
6 
6 

6 

7 

10.  17101 

17087 
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17045 

9.  96078 
96104 
96129 

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ii 
ii 
II 

12 
12 

10.  03922 
03896 

03871 
03845 

03820 

10.  13179 

13191 

13202 

13214 
13225 

5 
5 
5 

6 

9.  8682  1 
86809 
86798 
86786 
86775 

35 
34 
33 
32 
3i 

3° 
3' 
32 
33 

34 

6  20  o 
19  52 
19  44 
19  36 
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5  40  o 
40  8 
40  16 
40  24 
4°  32 

9.  82968 
82982 
82996 

83010 
83023 

7 
7 

8 
8 

10.  1  7032 
17018 

17004 
16930 
16977 

9.  96205 
96231 
96256 
96281 
96307 

13 
'3 

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10.03795 
03769 
03744 
03719 
03693 

10.  13237 

13248 

13260 

13272 
13283 

6 
6 
6 
6 
7 

9.  86763 
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86740 
86728 
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30 

29 

28 

27 
26 

3 

37 
38 
39 

6  "19  20 
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12 
12 
12 

13 

•3 

10.  15115 
15102 
15689 
15077 
15064 
15^51 

9-99874 
99S99 
99924 

99949 
99975 

IO.OOOOO 

23 
24 
24 
24 
25 

25 

10.  00126 

OOIOI 

00076 
00051 
00025 
ooooo 

lo.  14988 
15001 

15014 

15026 

15039 
15051 

1  1 

12 
12 
12 

I2. 
12' 

9.  85012 
84999 
84986 
84974 
84961 
84949 

5 
4 
3 

2 

i 

0 

M. 

Hour  P.M. 

Hour  A.  M. 

Cosine. 

Diff. 

Secant. 

Cotangent. 

Diff. 

Tangent. 

Cosecant. 

Diff. 

Sine. 

M. 

134°                                                             45° 

222 


INDEX 


A 

PAGE 

Altitude,  apparent 39 

circles  of  equal £3 

correction  for 39 

meridian 41 

to  take  an 38 

true  S9 

Amplitude 61 

B 

Barometer  69 

mean  level  of 71 

Beacon 91 

Bearing 10 

compass  11 

conversion  of  one  to  the  other  — 11 

cross 21 

bow  and  quarter 22 

magnetic 11 

of  one  object  22 

sailing  directions  by 22 

true 11 

Bells 94 

Buoys 87 

distinction  of  87 

names  of 87 

whistling 95 

bell 95 

C 

Cannon  . .   , 93 

Chart,  characteristics  marked  on 18 

currents  how  marked  on 14 

how  engraved 14 

Mercator's,  advantage  of 13 

signs  and  abbreviations  on  17 

tide,  how  marked  on H 

use  of    12 

use  of  different  sizes ., 16 


224  INDEX. 


PAGE 

Chronometer 35 

error  and  rate  of 36 

Clouds 65 

forms  of 65 

Collisions  at  sea,  regulations  for  preventing 98 

Compass 5 

azimuth 8 

bo  ff\ 5 

boxing  the  7 

card  5 

cardinal  points  of  the 6 

deviation  of  the 8 

lubber's  point  of  5 

needle 5 

points  of  the  6 

points  of  the,  in  degrees 7 

standard  8 

steering 8 

total  error  of ... GO 

Course  10 

compass 1 1 

conversion  of  one  to  the  other 11 

made  good 26 

magnetic  11 

shaping  the 24 

true  11 

Current  74 

drift 75 

sailing  76 

stream  75 

D 

Date,  astronomical 40 

civil  40 

Declination  40 

Departure  2(3 

taking  the 25 

Deviation 8 

table  of 1-2 

to  find  the  9 

Dip  39 

Distance  made  good  26 

meridian  zenith  41 

E 

Equator 13 

celestial 40 

G 

Gale,  straight  line 69 

Gongs 93 


INDEX.  225 

H 

PAGE 

Hygrometer 71 


Instruments,  use  of 1 

Icebergs 76 

L 

Latitude 13 

parallels  of 13 

Lead,  deep  sea  2 

hand 2 

Leeway 10 

Light,  character  of 79 

colored ...  83 

double 1 83 

fixed 79 

flash  or  intermittent  83 

house . . .   77 

order  of 79 

range  of 84 

revolving 79 

ship's 86 

ships,  how  appear 86 

Line  of  position 54 

error  of  compass  by 61 

Log  2 

adjustments 4 

book 25 

chip 2 

glass 4 

ground 5 

heaving  the 4 

line 3 

patent  5 

slate 25 

M 

Meridian 13 

celestial  < 35 

first  or  prime 13 

N 

Navigation,  definition  of 1 

P 

Parallax 39 

Poles  of  the  earth  13 

of  the  heavens  .  35 


226 

R 

PAGE 

Refraction 39 

Rockets 93 

S 

Semi-diameter 39 

Sextant  36 

adjustment  of  the  37 

index  error  of  . .   38 

to  take  an  altitude  with 38 

Siren 96 

Sound  signals  93 

importance  of 96 

effect  of  atmospheric  conditions 96 

Storm 68 

approach  of 72 

centre  of,  to  avoid 74 

centre  of,  to  locate 73 

direction  of  track  73 

revolving ...  69 

semicircle  of  74 

T 

Tables,  Explanation  of 109 

Thermometer  71 

Tide,  causes  of 

ebb 

flood 

neap 

time  of  high  tide,  how  found 15 

Time,  apparent 

equation  of 46 

mean 46 

Trumpet •  • 

V 
Variation —  • 

W 
Whistles 96 

Z 
Zenith..  35 


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